Tuesday, 23 September 2014


Yesterday my summer holiday officially ended. I packed my things into my Mum's car, left my hometown and moved into my new Uni accommodation. On the journey, Mum and I were trying to remember what had happened over the summer. It was really hard because the beginning of the holidays felt so far away. It felt like a year since we had made the journey to Coventry, rather than the few months it has been.

This summer, I found out that I was no longer staying on the four year course of my degree, but instead was being moved down to the three year course. I wasn't really too upset by this - I actually had still not decided which one I wanted to do and this just made the decision for me. It did mean, however, that I was one year closer to entering the real world and finding a job and all that stuff. There is where lies a problem. I have no idea what I actually want to do. I am not career driven in any way. I am more driven by family. I am also incredibly doubtful of my confidence to do things, especially social things. I am very shy and as a general rule don't really know what to say to people.

At the beginning of the summer, I tried writing weekly targets and publishing them on here so that I wouldn't just waste the summer doing nothing and actually trying to make myself better. I didn't keep up with it very well, so I don't think that is a technique I am going to keep up, but I did manage to achieve some things that I am proud of.

Fordhall Farm

After finding out that I couldn't go to Portugal, I had to rethink my work experience plans. I sent an email to two local community led organisations asking if I could do some volunteering. I heard back from one of them and after going in for a chat we decided that there wasn't really much I could do that would benefit me in the way I wanted, so I waited for the other to get back to me. Eventually they did, and I went in for a chat and came out with an agreement I would go in on Mondays and Thursdays to work in the office of the Fordhall Community Land Initiative. For the first couple of weeks, the main office administrator gave me lots of jobs to do like stuffing envelopes, checking databases and checking receipts against accounts. Once I was shown how to do a job, I worked hard to do it quickly and correctly, and didn't complain at boring jobs (like stuffing envelopes). I actually didn't really mind them that much.

After the first couple of weeks, the main office administrator actually left for a new job, and one of the long term volunteers also left to do other work. This would have been ok, except there was a big annual event planned for the next weekend - FordFest beer festival. Also, the woman in charge of running the event hurt her knee, so couldn't really move on account of being on crutches. I volunteered to come in extra to help out. I ended up coming in every day the week leading up to the festival, which is very hard when you aren't used to it.

During that week, I took on more responsibilities. I opened and processed the post every day, which included setting up new direct debits. I had to answer the phone and even phone up some people, which is totally outside of my comfort zone. I actually get heart palpitations at the thought of having to phone someone. I helped out a lot with general FordFest preparations, like making up band packs for all of the bands playing. It was hard work, but I enjoyed it.

My Mum is a firm believer that taking opportunities creates new opportunities. I have to say that I agree completely, because if I hadn't asked to volunteer at Fordhall Farm, if I hadn't asked about the acoustic set, I wouldn't have gotten the opportunity for Liberty and I to sing at the festival, and we wouldn't have had the opportunity to play on the main stage rather than the little unamplified stage we were expecting when one of the acts didn't turn up on time. It was terrifying and amazing at the same time.

At the end of my work experience, I was given a Certificate of Generosity as thanks for the 65 hours of work I put in (I checked Mum, 65 is right!) It's only a piece of paper, but I really appreciated it. I have also been promised that I will be contacted about FordFest next year, so I look forwards to that!


As well as playing at FordFest, I have been involved in various musical things this holiday. I sang a part in my younger sister's arrangement of A Thousand Years by Christina Perri to help her see how it would sound all together before she presented it for her house competition at school. I finally wrote the music to a song that I have been writing for 2 years, and have remembered why I love writing songs. I have inspired a little girl.

When I went to work at the boyfriend's mum's nursery, I brought my guitar along and played Stand By Me. A few weeks ago, when the new school term started, the boyfriend's mum said that one of the little girls that had taken to me came up to her with a ukulele and told her that she was getting her dad to learn some songs on the guitar so she could sing with him, and that she now knew all of the words to Stand By Me. That just made me melt inside a little bit. Music is a very important aspect to my life and I'm really happy that I inspired someone else with it.


As you know, I have recently (well, for the past year) gotten into running. Unfortunately, I have a lot of problems with my knees, so I haven't been able to do much running. Instead of just giving up, I have been working at other things to try and strengthen myself up for running again - something that a couple of years ago I would never imagine myself doing.

I started going to a circuit training class, and surprised myself by enjoying it. I have honestly never sweated so much as when I go circuit training, and I often hurt for days afterwards, but I enjoyed it non the less.

I joined an archery group. I have always been interested in archery, but never managed to stick with it. I apparently have some natural talent for archery, and joining the club in my home town has made me more determined to join up again at Uni and actually stick with it. Maybe even join in a competition!

I downloaded a 30 day challenge app. Ok, so I have yet to actually complete any of the challenges, but each time I restart, I am still doing something. I realised that my needs changed, so picked a different exercise to do. Currently, I am doing push ups (girly style I'm afraid, I can't even do one properly) for my upper body to help with archery, plank for my core to help with general strength and running, and squats for my legs to hopefully help with my knee problem.

Now that I'm back at Uni, I am going to try and complete the beginner's training program that my family did with their running club. I'm trying to build up my speed and my stamina, as well as strengthen my knee of course. I went for my first run yesterday, and managed to go 1.6 miles, with my knee only starting to hurt in the last run/walk section.

In an effort to not waffle on for too long, I am going to leave it here. I may write a second part if I think of more things that I think are important, but for now I will just say that I think I have managed to grow and mature this summer. Usually when I leave for University I am really depressed during the week leading up to it and I cry when I leave my boyfriend and my Mum. I did have a cry on the Saturday before I left when my parkrun plans fell through, which was probably exacerbated by the fact I was leaving in a couple of days, but when I left my family I only felt sad for a little while. Of course I miss them, but I know I am seeing them again on Friday (which probably helps) and I have lots of exciting plans for the year ahead.

Thursday, 14 August 2014

Story cube 3 - bumble bee, person dancing, a burst

On his way to collect nectar from the flowers, Bumble always liked to stop in the garden and watch the humans. They were strange creatures, with only two legs and two feelers, standing upright whenever they walked. The rest of the hive warned Bumble about the humans, but his curiosity always drowned out their voices in his mind. How bad could they be really? They couldn’t even fly.

There was the Man, the Woman and the Smaller One. Bumble didn’t know if it was male or female. There was nothing to set it apart either way. It spent all of its time making loud noises or sleeping.

Today, they were all outside. The Man was spraying water from a strange long, green thing all over the garden. The Woman was holding something in her feelers, staring at it non-stop, only pausing to flick something over then resume staring at it. Bumble had no idea what that was. The Smaller One was sitting in the grass, pulling it up and dropping it on its head. It made a loud gurgling sound each time that made Bumble feel happy. He didn’t know what the sound was, nor why it made him so happy, but he wanted to hear more.

He decided to get closer. Bumble usually kept his distance from the humans. He was unsure how they would react to him and obviously the warnings from the hive had had some effect on him. Today was just too much though. He had to know more.

As he got closer, he saw the Smaller One look up at him. It reached its pudgy feelers towards him. Its face didn’t seem evil. In fact, it looked like it was friendly, so Bumble landed on top of its feeler. There was no fur on the Smaller One’s feeler. It was just covered in a warm, fleshy substance that was kind of sticky. The Smaller One was bringing its feeler closer to its open mouth.

Suddenly, Bumble heard a high pitch noise come from the direction of the Woman. Then there was a waft of air that rushed past him, causing him to take to the air in shock. What was going on? The Woman was now holding the Smaller One, who was making that loud noise again. Its face was all screwed up and going red. Where was the Man?

Just as Bumble turned round to look for the Man, he felt another waft of air. This time he was pushed sideways. The Man was waving his feelers around. He looked ridiculous. Bumble had heard that humans sometimes moved like this when there were harmonious sounds playing, but he couldn’t hear any now. Bumble moved in and out of the Man’s flailing feelers, but eventually one hit him.

Bumble felt a smack and his vision flashed white before him. He felt himself soar through the air, but was powerless to stop it. He landed in a flowerbed with a bump. He lay there for a while, gathering up his strength, lying still in case the Man came looking for him. He didn’t want to be found.

He had no idea how long he lay there, but after a while he could no longer hear the humans. They must have left the garden, so Bumble got up slowly and flew to the top of one of the flowers. After a quick glance around to make sure he was really safe, Bumble shot off back in the direction of the hive.

He would never stop to watch the humans again.

Sunday, 10 August 2014

Weekly Update

So far this week, I have done:

1 - Write story cube story 5 (bonus: try and write the one I missed too)
2 - Write types of numbers post
3 - Find more ideas for future types of numbers posts
4 - Go to work experience on Monday with enthusiasm
5 - Come out of work experience on Monday feeling like I have achieved something
6 - Go for a run - hopefully without too much knee pain
7 - Go on an adventure to find an archery store
8 - Read a chapter of a book - any book, I don't read enough
9 - Go through tax returns with the boyfriend's mum
10 - Do my archery exercises everyday

Well, the story cube is just a draft, but I've written it a lot earlier than I usually do, which is a big improvement on my failure to do it last week. I managed to read a chapter of my Bedside Algebra book and we found the archery store that had been recommended to us. Mum bought me an arm guard and a finger tab as the birthday present she owed me. We didn't get any more than that because the man in the store happens to be coming to the club that we shoot at, so he said he would be able to help me out more after he has seen me shoot. Who knows, maybe this time in a couple of weeks I will have my own bow! I'm not going to lie, that would be awesome.

I have done my archery exercises every day so far, except today, but that's because I did actual archery so I think I can forgive myself for that one. I could definitely tell that the exercises I have been doing are making a difference to my strength. I even almost have a muscle on my right arm!

Tomorrow I start my work experience. I'm quite nervous about it because my brain likes to go into overdrive and over think everything. If I don't know exactly what is supposed to happen, I start to panic. I don't know if I am driving, or if I can get a lift (which I would prefer - one less thing for me to worry about doing). I don't know where to park if I am driving. I asked, but I'm not sure I know which car park they meant. I don't know what it is going to be like working there. I think it is going to be interesting, but until I've actually done it, I am in try-not-to-panic mode. I'm going to write a post about it once I've done a week or so of work, so hopefully then I'll be able to say there was really nothing to panic about!

Thursday, 7 August 2014

Story Cube 2 - person playing with dolls, walking stick, person jumping off a ledge

Christie sat on the floor of her grandparent’s living room, playing with some dolls that had been left out for her. She didn’t really like dolls, but they were the only toys left over from when her mother was young, so they were brought out every time she came to visit.

What Christie really liked was stories.

She got that from her grandfather, who was currently sat in his usual spot in the big armchair, in front of the fire, reading a newspaper. Propped up against the wall beside him stood his gnarly old cane. Christie stared at it a while, then turned to her grandfather.

“Grandpa, why do you walk with a cane?” she asked him. He lowered his newspaper slightly, and looked over his glasses at her, with a hint of a smile on his face and a gleam in his eye. Christie knew the look well; it was story time.

“Well, you see sweetheart, I wasn’t always the doddery old man you know me to be. I was once an adventurer. I travelled all over the world looking for new and exciting journeys to take that would lead me where I least expected them to.”

Christie listened intently. Grandpa always told the best stories, and she could tell that today was going to be no exception.

“I was a young man, sailing across the sea as part of the crew on a small ship transporting a grand jewel back to England – the Wimueko. This jewel was priceless, so of course we had to guard it with our lives.
“All was going well until one fateful day. We had been suffering from a lack of wind, so had been rowing all morning. Rowing a ship, even a small one, is very hard work, so as you can imagine we had to stop for a rest. It was at this moment, when our guard was down, that we were suddenly ambushed by pirates! We rushed to arm ourselves, but the pirates were too quick. They had us surrounded. We were only a small crew, so they tied us to the mast of the ship. Then the captain arrived.

“Captain Ferdinand was the most feared pirate in them days. I recognised him at once by the scar across his nose, and the fact that he had different coloured eyes. One was a watery blue, but the other was a deep, dark black. There was evil in that eye.”

Christie shuffled closer to her grandfather’s feet. “What did you do Grandpa?”

“I did what any brave adventurer would do with something under his protection.” He leaned over his knees, close to Christie’s face, and whispered dramatically, “I challenged him to a duel!”

Leaning back in his chair so that he could gesture wildly with his arms, he continued with his story.

“There was just the two of us, circling each other, cutlasses in hand. All the other pirates gathered round to cheer on their captain, waiting for bloodshed. My blood. The fight began and we slashed at each other, high and low, jabbing and slicing, parrying and blocking. Just as one of us got the upper hand, the other would push back and level the playing field. It was a tremendous battle.

“Eventually, I got Captain Ferdinand cornered and pinned to the floor. The battle was won, and I was the champion. I stood over him and told him to leave and never come back! The pirates began leaving our ship, the captain following last. We thought we were safe, but at the last moment, the dirty rotten pirate turned and sliced at my leg, then left laughing on his ship.

The cut went deep, and became infected on the way home, but luckily the wind was on our side and we made a swift journey back. My leg was treated, but I have walked with a limp ever since.”

At this point, Christie’s grandmother poked her head through the door, announcing that dinner was ready. Christie jumped up and grabbed the cane for her grandfather then watched as he lumbered his way into the kitchen. As much as she loved hearing her grandfather’s stories, Christie also had a thirst to know the truth. Walking over to her grandmother, she whispered to her so that her grandfather didn’t hear, “what really happened to his leg Grandma?”

Christie’s grandmother looked over at her husband, then back to her granddaughter.

“Well,” she whispered back. “When he was a boy, he thought he could fly, so he tried to jump off the roof.”

Wednesday, 6 August 2014

Weekly Targets 6th August - 12th August

After the horror of realising that Sharknado 2 was airing the same time as in America, not when I thought it was, and watching the Shining instead, I accidentally forgot to set myself targets last week. I did however start a new thing with Liberty. She sent me a link to a post in relation to helping my time slippage, which was about this schedule that the person who wrote it sticks to to stay productive. We thought we would try it out.

I let Liberty fill it in today... Basically it is just a laminated schedule that I can write on each day with whiteboard pens. It is quite hard to stick to it exactly at the moment because each day I'm doing something different, but I think it will be really useful when I go back to Uni.

Anyway, this week I managed to go driving a couple of times (scary, I know!) even once on my own today (even more scary!!). I had an awesome time shooting balloon dogs at archery, with the instructors saying that I had advanced technique and joking that I could be the next Danielle Brown. I went to Ford Hall Farm and have sorted out getting some work experience there starting next Monday. I finished the second chapter of the accountancy book. Now onto this week:

1 - Write story cube story 5 (bonus: try and write the one I missed too)
2 - Write types of numbers post
3 - Find more ideas for future types of numbers posts
4 - Go to work experience on Monday with enthusiasm
5 - Come out of work experience on Monday feeling like I have achieved something
6 - Go for a run - hopefully without too much knee pain
7 - Go on an adventure to find an archery store
8 - Read a chapter of a book - any book, I don't read enough
9 - Go through tax returns with the boyfriend's mum
10 - Do my archery exercises everyday

Can you tell I'm getting slightly obsessed with archery?

Monday, 4 August 2014

Types of Numbers - Taxicab numbers

There was a mathematician named G. H. Hardy, who discovered and then later worked closely with a brilliant young mathematician named Srinivasa Ramanujan. One day in 1918 or 1919, Hardy went to visit Ramanujan in his private nursing home. Hardy said about Ramanujan:

"I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me a rather dull one, and that I hoped it was not an unfavourable omen. 'No,' he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways'."
 This can be generalised to the following definition:

Ta(n) is the smallest number that can be expressed as the sum of 2 positive cubes in n distinct ways.

These numbers have been dubbed Taxicab numbers in honour of this anecdote. At the moment, only 6 taxicab numbers are known. The first few, with the cubes that make them up, are:

Ta(1) = 2 = 1^3 + 1^3

Ta(2) = 1,729 = 1^3 + 12^3
                      = 9^3 + 10^3

Ta(3) = 87,539,319 = 167^3 + 436^3
                                = 228^3 + 423^3
                                = 255^3 + 414^3

The remaining three known taxicab numbers are 6,963,472,309,248, 48,988,659,276,962,496 and 24,153,319,581,254,312,065,344.

I would love to know how they discover which number is the smallest one. Is is just a brute force algorithm that goes through every possible combination of cubes for each number? Or are there ways to narrow down the variables? At a guess, I would say it is mostly brute force, as there has been a lot of time between the discovery of each new number, the latest one only being discovered in 2003.

Although we only know the smallest number for six equal sums of two cubes, it has been proven by Hardy and Wright that the number of sums can be made arbitrarily large. In other words, the list of taxicab numbers goes on forever. There is not a biggest taxicab number.

Some people take taxicab numbers to be the list of numbers that are the sum of two cubes in two or more distinct ways. The first few are 1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, ...

I can see how you could find these numbers. You would have to limit the number you look up to, say to N. Then you take every cube number between 1 and N and add them to 1. Next add every cube number between 2^3 = 8 and N and add it to 8. Do the same up until N^3 + N^3, then sort all of the sums into order of the answers. Then you can go through the list and see which sums have the same answers. Obviously this would take very long to do by hand, but hey, that's what computers and algorithms are for!

Thursday, 31 July 2014

Story Cube 1 - hag, man in a portal, birdcage

I wake up, sweating, heart pounding. Thank god for these cool metal bars I can press my face against. What actually happened? I was dreaming, yeah dreaming, that was it. But what about? I’m breathing too hard to think clearly. I need to calm down. Calm down…


There was a woman; I think it was a woman anyway. She was… like a… a hag. Yeah, a hag, but her face was covered by a heavy hood. What was she doing? I can’t quite remember. Why is it you instantly forget a dream when you wake up? She was in a gloomy room, a kitchen I think, although not a standard one. No ovens or fridges, just… a cauldron of some kind? It seemed normal at the time. She was mumbling something too, but I couldn’t make out the words. No, I can’t think what they were. She was moving round the cauldron. She knocked a birdcage that was hanging from the ceiling and left it swinging while she collected strange items from the shelves in the room. Colourful bottles, full of thick viscous liquid; odd plants I had never seen before, dried and curled like talons; and rabbit feet? Something small and furry anyway. Each one produced a new puff of smoke and different smell as it was added to the concoction being created in the cauldron.

So where was I in all of this? Certainly not helping, so what then? I must have been in the room, I was watching. But I didn’t move, no… I couldn’t move. I was tied up in the corner of the room, on the floor. I remember because I had to look up to see what she was doing, even though she was hunched over, almost in half. She never looked my way. Not once, until…

What happened? She stared at me. I can’t remember her face, just her eyes. They weren’t human. They felt like they were piercing my soul. Then I saw nothing. Only a swirling vortex of colours - red, blue, purple, black - spinning round me faster and faster. I felt myself lift from the ground, seeming to compress as I flew higher and higher. I didn’t feel right in my own body. Everything felt… smaller. How could that be? How…

I’m not in my bed.

I’m not… I’m not in my bed. Where…?

Cool metal bars…

I’m in the birdcage.

Tuesday, 29 July 2014

Work Experience - Forton Nursery

My boyfriend's mum owns a nursery. It is a cute little place near Newport, which achieved outstanding in their latest Ofsted inspection, and over the last few years I have helped out at various summer fayres and things outside of school time. Now you know that I have been looking for things to push me outside my comfort zone and to gain a little work experience, so when she asked if anyone was available to help out for a couple of days, I volunteered.

I may not know what I want to do with my future career, but I am pretty sure that I don't want to be a teacher. I don't think I'd be very good at it, and to be honest, Liberty has kind of put me off! So I didn't volunteer with the thought of "I'll get some experience working in a school to help me be a teacher". I just thought that experience is experience, even if it is not what I want to do in the future.

The first day I was there, I helped to set up the tables with different activities for the day. I spent most of the time trying to build a zoo out of duplo, which was harder than it sounds as there were more blocks and animals than table surface! As the kids arrived a few helped me out a bit, although most just looked at me rather warily. I think they know the boyfriend's sisters quite well as they are around more, but they had never met me.

Throughout the day I mostly just picked up toys from the floor to keep it from getting too messy (and to stop the ukulele from being trashed!) At one point I was helping one boy to cut out pictures to stick into his story book about moving to primary school. He spent most of the time nearly cutting off my fingers and gluing my hand to the paper. He kept getting distracted too, but I managed to keep his attention on his book until he finished it.

I was shown where the outdoor toys were kept and how to choose what should be brought out so that when I came later on in the week, if I needed to I could get the toys out by myself while the teachers were busy with the kids indoors. When we did go outside, I pushed the swings and chatted with some of the kids about random things like trying to guess my age and how many sisters I have.

On the first day, I mostly felt like I was just playing, but the boyfriend's mum said I was big help. I think it was because while I was keeping an eye on things, she could get on with some important things in preparation for a trip later on in the week without distraction.

When I came back later in the week, I was in charge of making popcorn for the "cinema room" where the kids were watching Frozen as an end of year treat. Of course, you give a child a cup of popcorn, they eat it too quickly and immediately start hassling you for more. Multiple that by 15 and that's what I had! I had to make them a fruit pot, then make sure they ate that before they could have more popcorn. When they know there is popcorn, fruit doesn't seem like a good option, so that was interesting! I managed to convince most of them to at least try the fruit.

While they all went outside to play, I washed up the dishes from snack time. As it was a hot day, they kept coming back in, asking me to fill a watering can so they could cool off.

I had brought my guitar in that day so that we could do a little music session. I was expecting some of the teachers to lead and me to just play guitar like I had done one other time when I came in just to play guitar, but the boyfriend's mum told me to take the chair and to lead the group while they did other stuff. I had never done something like that before, so I didn't really know what to do. I found a few songs that I knew in the songbook, and got the kids to sing along with me (the teachers sang along to get them started thankfully!) and then I tried turning it into more of a game. I got them to do the actions, and to sing as fast as they could to race me, and things like that. I think they enjoyed it. Most of them joined in, a few were even quite enthusiastic, especially when we were singing really fast.

When we ran out of songs to sing, we still had a few minutes before lunch, so the teachers said to just play anything. I don't normally remember chords for songs, but I do know Stand By Me (it has 4 chords in the same progression all the way through!) so I sang that. I have never had a group of people listen to me singing so intently before. They liked it so much that when I finished, they asked me to do it again!

I really enjoyed helping out at the nursery. A couple of the girls became rather attached to me, one of them said "I'll miss you!" as I left on what was supposed to be my last day. The next day was the last day of term and I asked the boyfriend's mum if she wanted me and Ivy to come in a play guitar at the picnic they were having. My idea was to get the kids to sing Let It Go from Frozen with me as a surprise for her (they made her cry when they sang along with the film) but she kind of ruined it by asking if we could practise it with them to sing for the parents. Never mind!

We went in the next day and basically did the same as I had the day before and distracted the kids with singing and singing races while the teachers set up for the picnic. We sang through Let It Go so many times that my already sore throat was barely working, but it was a lot of fun. When it came to the actual performance the kids were great. It was very funny because it was obvious where they didn't know the words. "LET IT GOOO, LET IT GOOOO, ..... LET IT GOOOOO" One of the parents came and told us that having the guitar and the song made the day a little bit more special, which felt really good. That day was also good because one of the girls came up to me specifically to say goodbye (and give me a hug :)) and another (the one who said she would miss me) told me I was the best teacher.

Although I had a lot of fun, I don't think working in a nursery is something I could do all the time. Handling kids is much easier if you are only doing it in short bursts. I would be more than happy to go back and help out at Forton Nursery again though!

Monday, 28 July 2014

Types of Numbers - Vampire Numbers

This week I thought I would write about something slightly more fun, and less hard work to understand. I came across these numbers when I was on a website about maths careers, although apparently I had read about them first in Simon Singh's book - The Simpsons and Their Mathematical Secrets. I don't remember, but my mum has been reading it, so I will trust her! The numbers I am going to talk about are Vampire Numbers.

The Wikipedia page says that a vampire number is:

"a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains precisely all the digits from x and from y, in any order, counting multiplicity."

In English, this means that a vampire number is any whole number with an even number of digits (so it can be a 2 digit number, a 4 digit number, a 108 digit number, you get the idea...), call it v, such that there are two whole numbers with half the number of digits of v, call them x and y, where the digits of x and y are exactly the same as the digits of v in any order, and they multiply together to make v. We call x and y the fangs of the vampire number. The fact that the fangs do not have trailing zeroes just means that the fangs can't both be divided by a factor of 10 to give a whole number. For example, 600 and 740 have trailing zeroes because you can divide both by 10 to give 60 and 74.

I think it is easier to see what I mean with an example of a vampire number. Take v = 1260. This is actually the first vampire number. You can see that it has an even number of digits (4), so the fangs will both have 2 digits. If you have x = 21 and y = 60, you can check that 21 x 60 = 1260. Also, 21 and 60 use the exact same digits as 1260. They don't have trailing zeroes (60 can be divided by 10, but 21 cannot), so this satisfies all of the conditions for 1260 to be a vampire number.

The list of vampire numbers is infinitely long, meaning you can always find another one, your list will never be complete. I don't know how this has been proved, but I would be interested to find out. Vampire numbers are a relatively new concept in maths, only being written about for the first time in 1994 by Clifford A. Pickover.

Some vampire numbers have more than one set of fangs. For example, 125460 has two sets of fangs: 204 and 615 or 246 and 510. I will leave it to you to check that they satisfy the conditions!

There are also different types of vampire numbers, such as prime vampire numbers where the fangs are both prime numbers.

As far as I'm aware, vampire numbers have no mathematical significance, other than the fact they are rather beautiful things. Numbers are weird, and I love all the patterns, constructions and strange coincidences you can find within them.

Sunday, 27 July 2014

Midweek Update

Here is what I've done so far this week:

1 - Write story cube story
2 - Write types of numbers post
3 - Write a post about work experience at nursery
4 - Paint the fence
5 - Work out how to use linkedin and start finding people to contact
6 - Work my way through at least the next chapter of the accountancy book
7 - Go to Festival Drayton and try to arrange some work experience
8 - Perform at open mic night at the Beer Festival
9 - Read at least one chapter of the Bedside Book of Algebra
10 - Go for a bike ride

I have painted the shed, which is a start on the fence (not sure whether the whole fence will get done this week or not, we are rather busy!) I have also started looking at chapter two of the accountancy book. I now know what double-entry bookkeeping means, and have started looking at how to record transactions. It sounds really boring, but I'm actually quite enjoying it. I know what I'm doing for my types of numbers post, and I have a slight idea for my story cube, but I haven't even thought about my work experience post. I realise that I should have done it earlier on in the week, but time just goes by so quickly. I haven't even had time to read! I have no idea when this bike ride will happen either... Maybe tomorrow afternoon, if I have time between shopping with Liberty and catching up on blog posts.

I did manage to go and talk to somebody at Festival Drayton though. I find it really hard to just go and talk to people, especially if I don't really know what I want to ask. But I went. Although they couldn't really help me with work experience particularly, I have said that they can call me if they desperately need someone to wash dishes or to usher for movies, which will throw me in with a load of new people and hopefully build my confidence a bit.

I also performed at the open mic night at the Beer Festival in a local pub that Ivy works at. Liberty and I decided to sing some duets together for some fun this summer, and we love to perform, so the open mic was a good opportunity to get back into singing a little bit. It was ridiculously hot, very crowded and the sound setup wasn't very good, but I had fun just singing with my sisters again (I did a song with Ivy too). Hopefully we will get more opportunities in the future.

Wednesday, 23 July 2014

Weekly Targets 23rd July - 29th July

So after the bad start this week, I managed to complete most of my targets. The only ones I missed were finishing the analysis notes, finishing the targets from last week that I didn't manage and the one about linkedin. I have actually joined, but I can't work out how to use it. Now that my stepdad is back from Brighton, I am going to ask him to have a look at it with me, so hopefully I will have more luck with that soon. I did go through some more of my notes, but it has been so warm that I've been finding it hard to concentrate on anything other than trying not to melt and just enjoying the sun. My chalkboards are nearly finished, they just need a couple more coats of paint I think. I would have trimmed the hedge at some point had my stepdad not beaten me to it...

Here are my targets for this week:

1 - Write story cube story
2 - Write types of numbers post
3 - Write a post about work experience at nursery
4 - Paint the fence
5 - Work out how to use linkedin and start finding people to contact
6 - Work my way through at least the next chapter of the accountancy book
7 - Go to Festival Drayton and try to arrange some work experience
8 - Perform at open mic night at the Beer Festival
9 - Read at least one chapter of the Bedside Book of Algebra
10 - Go for a bike ride

As I'm not really sure about how well I've managed time slippage, I am going to set that as my bonus target for the week.

Monday, 21 July 2014

Types of Numbers - Imaginary Numbers

Last week I told you about the building blocks of numbers, the number line. I also said that these numbers are not sufficient to solve every equation possible. Imagine you had the equation:

x^2 = -1

(You probably know x^2 means x squared, but I just thought I'd check!)

At this point you are probably thinking, "but you can't have a negative square number," which is absolutely right, if you are dealing with real numbers. So the answer to the question of how to solve the equation is to not look at real numbers. This is where imaginary numbers come in.

An imaginary number is represented by the letter i. i is equal to the square root of -1, so as you can probably guess, the answer to the above equation is in fact:

x = i

This is a very strange concept for some people, because imaginary numbers are not something that you can imagine in real life. Whole numbers, fractions and even irrational numbers are easily translated into real life problems, but imaginary numbers are an abstract concept.

There is another type of number that uses imaginary numbers. These are called complex numbers. These are simply numbers of the form a + bi, where a and b are real numbers. All previous numbers I have talked about are complex numbers too. If we take a or b to be equal to zero (in maths, or usually means one or both) then we can see how real numbers and imaginary numbers are both of the same form as complex numbers.

Complex numbers can create some very beautiful things. For example, take the Mandelbrot Set.

Mandelbrot Set

Zoomed in
This is an example of a fractal, which is created by feeding the result of z^2 + c (where z and c are both complex numbers) back into z.

Sunday, 20 July 2014

Midweek Update

Here is what I've done so far:

1 - Write story cube story (this is a weekly thing, not the same story or cubes!)
2 - Write types of numbers post (also a weekly thing)
3 - Do my leg stretches every day
4 - Go bowling with the boyfriend
5 - Finish the targets I didn't manage last week
6 - Join linkedin and look for Warwick maths graduates to contact and get information from
7 - Finish the first week of analysis notes and start the second week
8 - Read the first chapter of the accountancy book I got from the Library
9 - Read a chapter of the Bedside Book of Algebra
10 - Try and manage my time slippage

That really doesn't look like much does it... I don't think I've been doing very well with my time slippage. I get distracted easily with everything else going on in my life: grandparents visiting, running, various other things. I did work a couple of days at the boyfriend's mother's nursery (more about that in a later blog post) so it wasn't a complete waste of time.

I have started a few things. I have nearly finished the first chapter of the accountancy book (kind of enjoying it so far), I have started writing the types of numbers post and I have been doing my leg stretches every day. Well, I might have missed one day, I can't remember if I did them in the morning or not, but Liberty and I have a new exercise regime which includes yoga and calf stretching, so I think I made up for the potential missed day.

The boyfriend and I had a really nice day when we went bowling. I absolutely suck at bowling, but we had fun and then had a game of pool (which I won!) and played in the arcade for a bit. The shooting game was ace, although it kind of made my arms ache after a while. My original plan was to make a picnic and go sit in Telford Town Park, but it was pouring with rain, so instead we went to Frankie and Benny's. The food was really good, and it was nice to do something a little bit different than we usually do.

Tomorrow I hope to get a few more things done from my list, hopefully getting back on track.

Wednesday, 16 July 2014

Weekly Targets 16th July - 22nd July

Of the ten targets I set myself last week, I completed six, I started two, one was changed, then changed back, and sort of done, and only one didn't get started because we didn't find a good moment for it. So I think that was pretty good.

In case you are wondering, I didn't trim the hedge, and the one that got changed was to send out the cover letter to at least 2 local companies. This got changed around because I was meant to be going to Portugal, so there wasn't any point in doing it, but now Portugal isn't happening, so it is relevant again. I went to the Job Centre today, and the lady there gave me some suggestions of who would possibly give me work experience, so I have emailed those (which is why the target was sort of completed).

The two I started were to go through my notes and to finish my chalkboards, which I can hopefully do this week. So my new targets are:

1 - Write story cube story (this is a weekly thing, not the same story or cubes!)
2 - Write types of numbers post (also a weekly thing)
3 - Do my leg stretches every day
4 - Go bowling with the boyfriend
5 - Finish the targets I didn't manage last week
6 - Join linkedin and look for Warwick maths graduates to contact and get information from
7 - Finish the first week of analysis notes and start the second week
8 - Read the first chapter of the accountancy book I got from the Library
9 - Read a chapter of the Bedside Book of Algebra
10 - Try and manage my time slippage

Monday, 14 July 2014

Types of Numbers - The Number Line

There are so many different types of numbers with amazing properties that make them just beautiful, but I wouldn't be able to talk about these numbers without the most basic of numbers. So I am going to talk through the different numbers that make up the number line. (I said number a lot in that paragraph didn't I?)

First of all, we have the natural numbers or counting numbers. These are, as the name suggests, the numbers used to count things: 0, 1, 2, 3, 4, 5...

Next, we have the integers. These are the negative whole numbers along with the natural numbers: ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...

Next are the rational numbers. These are numbers that are quotients of integers. In other words, numbers of the form a/b, where a and b are integers. There is an additional restriction where b cannot equal 0, since dividing by 0 causes all sorts of problems! Basically, rational numbers are just fractions: 1/2, 37/90, 3/4, -4/2 etc.

Next are the real numbers. These are the rational numbers along with numbers called the irrationals. These are numbers that cannot be written as a quotient of integers. They are numbers where the decimals don't terminate or repeat (in other words they go on forever without repeating). Any number that isn't rational is irrational. The most famous examples are: pi, e, the golden ratio and the square root of 2.

So these are the numbers that make up the number line. However, these numbers are not sufficient to be able to solve every equation. But more on that next time!

Sunday, 13 July 2014

Midweek update

One week in, and I'm already going to have to change my plans. But that is the way of life. If you are busy enough, things change. So here is how I've done so far.

1 - Write story cube story (for Writer's club)
2 - Write up 25 things I like about me post
3 - Write types of numbers post
4 - Read as much of the accountancy book as I can (especially chapter 6)
5 - Finish writing the generic cover letter
6 - Send out the cover letter to at least 2 local companies
7 - Go through the first week of Analysis notes
8 - Run the Dearnford relays
9 - Finish making my chalkboards
10 - Trim the hedge

I've actually only written a first draft of the story cube, but the main thing is done, so I'm counting that. I've also actually started the chalkboards too, but we ran out of time before the weather got too gloomy to paint outside. I am slowly reading some of the accountancy book, but it is kind of heavy going. I did borrow another book, more about how accountancy actually works than how to get a job in accountancy, because the boyfriend's mum said I could have a look at how she does her accounts, and let me have a go (she was very keen to hand it over!)

On Thursday, I went with my family to a race at Dearnford lake. It was a 2 mile relay in teams of three. My running had been suffering recently due to problems with my knee, and after epically failing to do parkrun the Saturday before, I was worried about doing this run. Luckily, the boyfriend's sister was more than willing to run with me, so even though I was going reeeeeally slow (coming 3rd to last and completing it only 2 minutes faster than a 70 year old lady), I did manage to make it round. I had to walk quite a lot, but I made it to a mile before the first bit of walking, so I was very pleased. It has taken until today for my knee to feel normal again, but I have found some leg stretches to hopefully help with my knee problems.

I managed to write my cover letter with the help of Liberty, but I have decided not to send it out, at least not yet. The reason for this is because I am possibly going to be doing some work experience in Portugal at the company my father works for. It is a terrifying thought, but would be really good for me. It would take me right out of my comfort zone, and that is what I need to try and build my confidence. I'm also going to work at the boyfriend's mum's nursery tomorrow and on Thursday, so that should be fun.

Thursday, 10 July 2014

Weekly Targets 10th July - 15th July

I am going to try an experiment. I really need to stay motivated this summer to be productive and make the most of the time I have over the holidays. The first thing I'm going to try is to publish a weekly list of targets every Wednesday on my blog, and to give a midweek update on my progress at the weekend. There will be different types of targets, designed to help me achieve the different challenges I want to face. Hopefully breaking it down like this, and having it out there on the internet will make me feel more accountable and more likely to stay motivated and productive. Also, it could help me when I go back to Uni to work the best that I can and get a good grade in my final year!

So, here are my targets for this week:

1 - Write story cube story (for Writer's club)
2 - Write up 25 things I like about me post
3 - Write types of numbers post
4 - Read as much of the accountancy book as I can (especially chapter 6)
5 - Finish writing the generic cover letter
6 - Send out the cover letter to at least 2 local companies
7 - Go through the first week of Analysis notes
8 - Run the Dearnford relays
9 - Finish making my chalkboards
10 - Trim the hedge

I know I've already done one of those things, but I'm a little bit late publishing the list! Will update at the weekend :)

Wednesday, 9 July 2014

25 Things I Like About Me

Recently, I have been thinking a lot about what I want to do in the future. Having just found out that I have to stay on the 3 year course, rather than the 4 year course at my Uni has really made me realise that I don't have all that long left before I have to go out into the big wide world of work. It also made me realise that I have absolutely no idea what I want to do, what I might be good at, nor how to go about finding out.

I know that I need to get more work experience, and while talking to my mum about it, it quickly became apparent that I have pretty much zero confidence in myself or when it comes to talking to people. I couldn't even ask my sister's boyfriend (who I have known for like, 10 years) if he knows if the police would take on someone for work experience because I didn't know exactly what I had to ask, nor how to go about starting that conversation. Every time there was a lull, mum would say "you could ask him now! I'm worried that you can't ask him" and stuff like that. But I just physically couldn't, and I don't know why.

Liberty is going through a similar thing as she is part way through changing jobs (fingers crossed she gets the one she wants!), so she is very keen on helping me out. My family got together and have started compiling a list of challenges for me to complete over the summer to help build my confidence so that I might be less pathetic when it comes to just talking to people, and hopefully along the way maybe get some ideas about what I want to do.

Yesterday, I completed one of the items on the list, which was, as the title of this post suggests, to write a list of 25 things I like about myself. I would like to share that here.

1) My eyes
2) My hair
3) I love my family
4) They love me
5) I love to sing
6) I started running
7) I have nearly overcome my weird eating problem
8) I'm smart
9) My smile
10) I play piano
11) I play drums
12) I play guitar
13) My sense of humour
14) I'm good at logic puzzles
15) I got a 2:1 in my first year of Uni
16) I got 74% for my second year essay
17) I ran all the way round 10k in 1 hour 10 minutes and 4 seconds
18) I have 31:01 PB on the Telford parkrun
19) I won performance of the year in my first year of Glee for singing I Knew You Were Trouble by Taylor Swift on elections night
20) I'm interested in magic - especially card tricks
21) I own at monopoly
22) I'm good at maths
23) I got a C in Art GCSE, even though I suck at Art
24) I try writing songs that aren't just cheesy lyrics
25) After 5 years, I still find more ways to be in love with my boyfriend

So there you have it, 25 things I like about me. Sorry about the mega cheese factor in the last one, he was complaining I hadn't written anything about him yet, so I thought I'd make it a good one!

Sunday, 18 May 2014


I have been wanting to start up my blog again for a while. I love reading my mum's blog (sometimes it's the only way I find out what is happening at home!), when Liberty writes something that isn't a review I always take a few minutes to read it, and I'm slightly jealous that they are such good writers whereas I usually just fail epically. If I have the words, I'm ok, but finding words to put to paper has always been difficult for me.

Today I have something I want to write about.

Last summer, I started running. Various members of my family and the boyfriend's family had been running for a while and, despite being a skinny twig, I wasn't very fit. My step-dad is a bit of a fitness fanatic and is always telling me how good a bit of exercise is for the brain as well as the body. So I thought, what the hell? I suck at sports, I'm not very well coordinated (odd for a drummer...) and any time I had to run, in sports or just going after a bus, my chest would close and I'd feel sick for like half an hour after the smallest distance.

Mum and Liberty are part of the running club in my home town, and part of that running club is a Beginner's Training Program. It's an 8 week program where you start off small, running for a minute, walking for 90 seconds and repeating 8 times, 3 times a week, and build up slowly until you are running for 30 minutes solid. I started off doing that, with the help of mum and Liberty, and anyone else who decided to join us. It was going well until 3 weeks in, when they got bored of running for just 3 minutes at a time, and mum decided "let's run a 5k route and see how far you can go!"

So that's what we did. I ran for 13 minutes before I needed to walk, and didn't ask how long we'd been going until 7 minutes in. That may not seem like much, but to me that was a massive achievement. I don't know how long it took to do that 5k, and the boyfriend drove past on the way so we stopped and had a chat. He offered me a lift, but I was determined to make it back myself!

I don't count that run as a proper 5k. Every Saturday at 9am, all around the country, there is an event called Parkrun. It is a timed 5k event, which you can sign up to for free. All you need to do is be there on time and bring your given barcode so they can scan it at the end along with your time. There happens to be one in a town close by to us, so we try to go as often as we can. My first parkrun, Liberty coached me all the way round. I ran for 2 miles before I needed to stop and walk, which was a record for me. At the end, Liberty and I were neck and neck for the sprint finish, with mum (who had already been finished for a while) squealing rather too excitedly as she saw us round the last corner. Being the awesome sister that she is, Liberty actually pushed me over the finish line at the end, just so I would have the faster time. I think it was a difference of less than a second in the end... But I had gotten round my first 5k in 35:13, which felt great.

It took a long time for me to get a faster time than that. Each subsequent parkrun was slower and slower, but I achieved other things instead. The second one I was running with my younger sister Charlie, helping her around the course for a fundraiser. One week we went to a different, much harder parkrun, and that was the first time I ran the whole way without walking. Yes, sometimes (a lot of the time I think) my running was slower than walking, but I did it. I even continued doing parkrun when I went back to Uni, which involved not only finding where the parkrun is, but getting out and doing it on my own. It's hard to get up and run when you don't have anyone to run with. But I absolutely love doing the parkrun. It is now something that we look to do whenever we go anywhere with one nearby. Recently Liberty, Charlie and I went to London to visit our father, and we even got up to do one there. That was by far the hardest course we've ever done. It had TEN HILLS! So Liberty and I got personal worst times with close to 40 minutes, but it was really beautiful and so much fun, so we didn't really mind! I have gotten several new PBs for 5k routes, my fastest so far being 31:01, which I am so pleased with. My goal at the moment is to try and run one in under 30 minutes.

Running has also pointed out other problems that I have with my knee. I've always had a bit of a bad knee, but it got to the point where I wouldn't be able to walk after a run because it hurt to move. Liberty had also been having trouble, and been to see a professional who said it wasn't actually her knee that was causing the problem, but the muscles in her legs being too tight. So now, not only do I run, but I have started doing yoga everyday for 30 minutes in an effort to stretch out my muscles more, to help me run better. I've gotten to the point where I can see how people can get obsessed with exercise. It's a really strange feeling for me.

Running has become a big part of my life. I like to go to sports shops and look at the accessories and running clothes you can get. Even though we didn't get to stay long, Liberty and I had a great time looking round the bit of the London Marathon Expo we made it to. I bought myself a leg roller massage stick thing, we got new running compression socks, we got fliers for other events and we tried a load of healthy food and drinks. And now, with absolute certainty, we can say our step-dad is crazy whenever he drinks beetroot juice. It may give you 5% extra oxygen level in your blood, but it is seriously gross! We enjoyed seeing Mo Farrah run past in the London Marathon (the boyfriend's mother is really jealous of that one. We were so close to the runners, it was ridiculous). I was so excited when my parents bought me a running watch for Christmas. I have had a water fight with Liberty at the unmanned water station in the Cheswardine 5 mile "fun" run. We didn't really run that one at all, but it was kind of fun how bad we were. I have dressed up as a reindeer with family to attempt to pull the boyfriend's sister, who was dressed as Santa, on a mobility scooter decorated as a sleigh around our town in a 5k Turkey Trot. That was hilariously bad. The mobility scooter had a speed limiter, which is slower than walking pace. The marshals had all left by the time we got round, and we cut out the last bit of the route. We so should have won the best costume though, we were robbed with that one.

All of the crazy things I have done since starting running has been great, but by far the best thing so far happened last weekend.

I ran a 10k.

My town, for the last 2 years, has been voted the top 10k route of the country. Last year, my mum, step-dad, Liberty, Liberty's boyfriend, my boyfriend, the boyfriend's mum and sister all took part in the race. I came home from Uni to support and to babysit my brother, and it was really a great day. So when the 2014 entry opened, even though I had only been running for a little while, I decided to sign up.

As race day came closer and closer, I was getting more nervous. I had never run that far, 5 miles being the furthest I had done. I was worried my knee would stop me, or stitch, or my new strange shoulder stitch (don't ask, I can't really explain that one). My aim was to keep up with mum, which I can just about do with parkrun now. I ended up running round with Liberty, and we quickly lost mum in the crowds. But I never really lost heart the whole way round. I got stitch during the ridiculously energetic warm up, so that was over and done with. My knee went stiff about halfway round, but didn't hurt while I was still running. I briefly got shoulder stitch, but that thankfully went away reasonably quickly. Having so many people cheering you on as you are running round really helps to keep your spirit up. We ran past our house where my grandparents, sister Ivy, and the two little ones were waiting with high fives. The boyfriend and his family were marshalling at the beginning (and so also at the end) of the course, and they are always ready with big encouragement. We saw Liberty's friend, our cousins unexpectedly, and someone I knew from school shouted my name out, which just really gave me an extra boost right after the demon hill Phoenix Bank. There was also a drum band which was playing in the town, but relocated to the top of Phoenix Bank, which was just genius placing. It really helped to get me up that hill. Once at the top of it, I knew there wasn't far to go to the end.

The course started and ended on the school field, and once we got there, I could actually see mum just on the other side, so we had managed to stay not too far from her in the end! I crossed the finish line in 1 hour 10 minutes and 4 seconds. It was the best feeling (helped by the fact I overtook a few people at the end :P) Liberty followed a few seconds after. Our aim for the 10k was just to make it round, running the whole way, but we said that if we beat Liberty's time from last year, it would just be the icing on the cake. Well, we smashed it by 3 minutes, and I ran the whole way!

I collected my goody bag, which included a bottle of water, a gingerbread man, a mars bar and a load of fliers, as well as a tray of yoghurts from the Muller factory in our town. My t-shirt is tucked away in my drawer, ready for my next run, and my medal is pinned proudly to my notice board.

I can't wait for next year.