ZERO: the Biography of a Dangerous Idea

Some of you know I have been reading this book ( Zero: The Biography of a Dangerous Ideaby Charles Seife) in the past month and I finished it just before the October holiday. So, I decided that it is just right to talk about it, especially because I loved it.

First of all, I think this is the first book I have read which talks about the history of just one number. To be fair, I thought it would be interesting from the description on the back – some books have great gripping descriptions on the back and this is one of them. I will copy a short paragraph from there:

The Babylonians invented it, the Greeks banned it, the Hindus worshiped it, and the Christian Church used it to fend off heretics. Today it’s a time-bomb ticking in the heart of astrophysics.


You can imagine I was quite impressed by this and really wanted to see what exactly it meant by all of that. I was not disappointed. It was one of the best maths related books I have read in a long time. It is gripping, interesting and shocking. It starts easily with a little bit of history of the number system we use now and how zero was not considered a number for a long time by many civilizations. I never thought that religion had such a big influence over mathematics over time and I was fascinated by this. Then the book gets to physics, chemistry and astrophysics, blending everything beautifully. I did not know how much this number has been shaking concepts from philosophy, religion, science and mathematics.

I totally recommend this book to absolutely everyone. You do need to know some basic concepts from higher mathematics (such as calculus) and things from physics (such as Einstein’s theory), but you will not regret it. I have to say it opened my eyes and I want to read even more about this. To finish this post, I want to share with you one of my favorite quotes from the book:

Cultures girded themselves against zero, and philosophies crumbled under its influence, for zero is different from the other numbers. It provides a glimpse of the ineffable and the infinite. This is why it has been feared and hated – and outlawed.


Hope you enjoyed this small, not that scientific and probably rambled post. If you want to talk more about books you can find me on Goodreads at Lthmath.  Let me know if you read the book and what are your thoughts about it. Thank you for your help and support. You can find me on Facebook,  Tumblr,  Google+,  Twitter and Instagram, I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy!


October Holiday

Today is my last day of the October Holidays. Here, in Scotland, there is a school holiday for 2 weeks in October. Therefore, I want to share with you what I did and how I relaxed (or tried to) during this holiday.

1. Visit many things. I have been living in this city for more than 5 years, but I have discovered that there are still many things I haven’t seen yet. Therefore, I have decided to visit 2 museums for this holiday.

The first one is the Zoology Museum and the small Botanic Garden close to it. I have to confess that I am not a big fan of stuffed dead animals, but I have learnt a lot about different species from this museum. Also, I have seen some beautiful butterflies (one of my favorite beings). Since I have discovered that butterflies are not killed to be stored, but that they take the dead bodies after their short lives, I feel better at this type of exhibitions. Also, I quite enjoyed and found fascinating all those skeletons on display. Moreover, if you are a mathematician and do not love corals (a fractal hint in there), seashells ( golden ratio hint ) and starfish (symmetry hint) I do not believe you. Here are some images:

The next museum was the Maritime Museum. I find it quite fascinating to read sea stories and to find more about the technology behind all of this. I confess I am quite scared of deep water in general and I find very interesting all the techniques to make things float on it. Because in the city the oil industry is still big, there are many things about this and also a little about renewable energy. Here are some images:

2. Reading is the best. I am a big book worm and I totally love reading, I don’t think I could live without books. So, this holiday I have decided to read the latest book by one of my favorite authors: The Sixth Watch: (Night Watch 6) by Sergei Lukyanenko. This is the sixth book from the Night Watch series and I loved it. Here is a small description:

They live among us. They fight among us. They are the Others, a supernatural race of magicians, witches, shape-shifters, vampires, and healers. Divided into the Light and the Dark, these rival factions have spent a millennium under a reluctant truce. Now, however, both sides must unite against the ultimate enemy.

Even though the description sounds like something not very new, I can assure you that it is way more intricate and interesting than it looks. To make it more interesting, let me just tell you that Light doesn’t meat Good and Dark doesn’t mean Bad.

 3. Video games are relaxing. I have not said anything about this previously on this blog, but I quite enjoy video games. I am not very good at it, but I can get stuck with a game for months until I move to another one. I will not go into much detail, but the one I have been playing a lot in the last months (and a lot this holiday) is StarCraft II.


4. More movies at the cinema. I did go more often to the cinema these 2 weeks and I kind of feel bad that I did not find more time to do this doing term time, but I am working on changing this. I have seen 3 movies and as obviously I have mixed feelings, but I will put them in order of preference: Deepwater Horizon (it is fast pacing, interesting and made me want to find out even more about the accident – I totally recommend it), The Magnificent Seven ( it was an old time good western and Denzel Washington is the best – a good movie to watch if you want to relax a little and especially if you are a western fan), Inferno (I have to confess I was not really impressed by it unfortunately, I have read the book a while ago and quite liked it, but the movie was not as good as I expected).

Hope you had a great weekend and if you have any book and movie recommendations of any type let me know in the comment box bellow. I would love to know about it. Also, what is your favorite relaxing activity for holiday? You can find me on Facebook,  Tumblr,  Google+,  Twitter and  Instagram. I will try to post there as often as possible.

What a Mathematician needs in the Kitchen

You know I am a big fan of any Kickstarter project which involves mathematics, even a drop of it makes me excited. This is what the campaign Polygons | The Flat 4-in-1 Measuring Spoon is all about.  The official description is:

Polygons is the origami-like measuring spoon that lays flat and folds to 4 different sizes to fit your cooking and baking needs.


First of all the name is quite mathematical: Polygons. Using the Wikipedia definition, “In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit.”  Well, interesting name and I kind of see why they decided to name it this way, but we have to be careful because a polygon is just about 2D shapes, while our spoon is a 3D one. But if we think about how the etimology of the word “polygon” (it derives from the Greek adjective πολύς (polús) “much”, “many” and γωνία (gōnía) “corner” or “angle”), then I quite like the name because the spoon really does change it’s look and shape depending on what you need.

Secondly, the origami part fits it quite nicely and I quite like the idea that you could have something like this in your kitchen.


The last thing, which kind of made me quite excited, is the fact that the shape is flat, not curvy. I know it is not about the shape, but the volume. I can think of quite some interesting maths problems on this. And I believe they had to do some interesting calculations to figure out how to make the shape so that it could hold the same volume as a normal spoon. What do you think about this? I would love to know your opinion in the comment box bellow. 


Absolutely incredible, show it so love on Kickstarter if you like the idea.

Have a great weekend.  You can find me on Facebook,  Tumblr,  Google+,  Twitter,  Instagram  and  WeHeartIt. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy!


Different Circles

I have not posted about an artist in a long time and I thought I should search for something new. So, I found this Italian designer Giuseppe Randazzo of Novastructura, who released a series of generative digital “sculptures” that depicted carefully organized pebbles and rocks on a flat plane.  The series of sculptures is titled Stone Fields and the works were inspired in part by similar land art pieces by English sculptor Richard Long.

It is very important to understand that this project has “started from a search for a 3D – objects optimal packing algorithm over a surface, but evolved in something rather different”, as the designer states. I don’t know much about the computer science part of this project, but I got quite interested in it because of the packing problems, a class of optimization problems in mathematics. The whole idea of these problems is to pack objects together into a container as densely as possible. If you think about area, we want to cover the shape as much as possible using different other shapes. These problems are quite important and are used a lot in real life: storage and any other transportation problems. People are interested to find out how many of the same object are required to completely cover every region of the box/container. Most of the time we don’t want overlapping… of course we don’t want to see an orange mixed with another orange in a box, we just want to see 2 different oranges.

Giuseppe Randazzo did some incredible work using some ideas from this optimization problem and the “sculptures” (computer generated in 2009, actual sculptures in 2014). Here are some images:

Hope you enjoyed this post and if you know about any artist with mathematical works let me know. Have a great day. You can find me on Facebook, Tumblr, Google+, Twitter  and Instagram. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy! 


10 Things I’ve learnt in my First Term of Teaching

I have survived my first term of teaching. In Scotland, the first term finished on the 7th and right now I am in a 2 week holiday (October Holidays). So, how could I spend my first week of holiday? “Still thinking about school” is the answer. Therefore I have decided to write about 10 things I have learnt about teaching, funny and serious at the same time.

1. Teaching is harder than I thought. I have to say that having my own classes with no one to help me or another teacher that could come in front on the room when things got out of control is not as easy as I thought. With all the practice I had last year, this is way different and sometimes it feels incredibly hard. There were moments when I thought it was to much for me, but hey!! there are also so many funny moments and exactly when I felt low a pupil did something unexpectedly nice, or the class decided to be nice and listen to me. Teaching is hard, but as long as I can see the good parts, things are going to be just fine.


 2. They don’t bring a pen/pencil. I have to say that this was the first thing I observed in my first week of school. And though now I sometimes find it funny, it is still equally annoying, but I cannot wait the moment when I will start saying: “I don’t have any more pencils in the class, so you have to do the work at home”. I think I will try this as an experiment once and see what happens, but I will definitely put the following poster somewhere in my class (priceless!!):


3. No names on the paper (homework or test). Some time in September, when I prepared my first class test, I just did not mention at the beginning of the test that everyone should put their names on the paper in front of them (for me it was an obvious thing to do). The problem was that I  ended up with 10 out of 27 papers with no names on them and it took forever for the pupils to decided who wrote which paper. Next test I did 2 weeks after I applied the rule “No name on the paper, no grade” – worked wonders!


4. The level of noise (talking especially) can reach maximum very quickly. I have improved a lot on this and now I have classes when people are working in silence (if it is an activity where silence is required), but in my first month I was desperate for silence. I think I will learnt more about this in time.


5. Never be scared to get in touch with parents. I have to say that I was quite scared first to email parents and I thought I was causing trouble for the pupils, but this is so NOT TRUE. I cannot say I have started doing this every day, but I have observed a lot of change in behavior after I talked with parents (good change). I just think that this should be done with moderation.


6. Never get extremely angry when they answer back. This was again one of the hardest thing to manage. Every time someone was rude and answered back I got so angry, like I never thought I would be. And it just escalated so quick for me. It is so hard to manage this but I have to always remind myself that getting angry is not the solution and I always have to stay calm.


7. They find out so many motives to get out of class. I never imagined that people can get so inventive when it comes to motives to get out of class. Starting with feeling sick to going to see another teacher about a project, I think I heard so many. The good thing is that I started to recognize the lies and it gets so funny to see their face when I say “no problem, you can go, but I will phone the teacher first”, or “it’s better to go directly to the nurse and phone your parents if you are feeling so bad”. I am sure I will hear funnier excuses and I just hope I will not start laughing when they say it.


8. Homework is optional. I have no idea why someone would think homework could be optional, maybe I was raised to know that this is a MUST, but I got quite a lot of people asking me about this… Hmm!!…


9. Extremely proud when something works. I could never imagine how proud and good I could feel after something turns up exactly how I planned for a lesson. It is the best feeling of them all. It is even better when pupils think they are just playing a fun game, when in fact they are learning something…. AWESOME FEELING!


10. Going to sleep is not that easy. To end this list, I have to write about “sleep”. I have no idea why, when I put my head on the pillow my brain decides to think about school and not go to sleep. This is sometimes so hard to manage and I am continuously trying out different methods to just fall asleep and not think about the lessons I have to do next day or worry if someone will do something stupid. I realized that it does not matter how much I think about it, there is always something unexpected in a school day.


If you have advice, just feel free to comment bellow. Hope you enjoyed this post. Have a great week. You can find me on Facebook, Tumblr, Google+, Twitter  and Instagram. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy! 


Vampire Numbers

This year I am planning a quite interesting Halloween day. I have already started searching for inspiration for my classroom and I am extremely excited for everything. I will write a blog post about this very soon, stay tuned. All this excitement of mine has transformed into another campaign on Teespring called Vampire Numbers.

If you thought that vampires have absolutely nothing do with maths, well a small girl from Romania (the land of Dracula) will tell you otherwise. The definition is not that hard to understand:

In mathematics, a vampire number (or true 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. x and y are called the fangs.

Even though I have not found many things about when these numbers first appeared and who came with the idea to call them “vampire numbers” and not something else, but I find them quite interesting. If you want to generate the first 25 vampire numbers (or more if you a total computer science fan), I totally recommend you take a look at the article Vampire Numbers from Rosettacode. If you want to find out more about these numbers, I recommend you watch the following video:

If I convinced you that these are great numbers, take a look at my designs from the Vampire Numbers campaign:

Hope you enjoyed this post and that you are excited for Halloween. Have a great week. You can find me on Facebook, Tumblr, Google+, Twitter  and Instagram. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy! 


What if?

There are a couple of things that changed in my life recently which made my reconsider my life and how I perceive the things around me. Therefore, I wanted to talk about one of the most important questions out there: what if?.


Thinking about my day to day life I am not really a big fan of this question. I don’t like questions such as “what if I haven’t done mathematics at university?” or “what if I have never moved from my home town?”. I find these the most annoying questions ever, absolutely not productive or helpful at all. There is absolutely nothing someone can do to change the past and the only useful thing is to “deal with it” even if it was a good or a bad decision.

On the other hand, questions like “what if I change the numbers in this equation?” or “what if I change the length of this line?” or “what if I change the gradient of this line, will it ever intersect the other line?” are crucial. In any type of science related subject the “what if” type questions are the most important. I have the feeling that if scientists would never ask themselves this type of questions, there would be absolutely no break trough, no evolution. For any new invention or discovery, you need to think at “what if” of the situation and start trying, researching more and more.

Therefore, encourage your children, students, pupils to ask themselves the right “what if?” questions. Start from an early age and build on. Use the question yourself in your every day life for random things, such as “what if I change this ingredient for the recipe?”. Encourage your child to ask questions, to be curios, to think outside the box. Never encourage regret and stupid questions. 

I know I have never really written this type of post and it is probably not the best ever, but I got a little annoyed by something in this past month. After I became a little more confident about teaching (I still have much to learn), I started asking “what if?” type of questions to my pupils and I was shocked by their refusal to think, participate in the discussion and, in general, their refusal to be curios. I am sometimes annoyed at their desire to just get the answer to the question and nothing else. I am trying to change things, but there are days when I cannot do it. I am and will be trying and so should all of us. We need curios people out there, we need curios scientists, mathematicians, we need them.

What do you think about this? Leave your opinion in the comment box bellow. I am very curios to find your thoughts about this. Hope you enjoyed this post and that you are excited for the future ones. Have a great week. You can find me on Facebook, Tumblr, Google+, Twitter  and Instagram. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy!