Algebra, General

Types of Numbers, part II

In the previous post we talked about how numbers have a varied social life, and they belong to different groups, like our chess clubs or gyms. In this post we’ll take a look at how we group numbers.

One of the most interesting groups of numbers is the prime number set, which is actually a subset of the natural numbers. A prime is a natural number with exactly two distinct natural-number divisors: one and itself. To make it more clear, a prime is a natural number that is evenly divisible only by one and itself. That is to say that if you divide a prime number by any other natural number you will get a fraction or decimal. We have a few conditions: a negative number cannot be a prime; and one itself is not a prime.

On the opposite part of the fence there are the composite numbers. A composite number is a natural number that has a positive divisor other than one and itself, which means that composite numbers are all the natural numbers that are not prime, except one. The number one is neither prime, nor a composite.

Also, I told you guys in the previous post that some numbers are perfect. Sounds nice, huh?  Well a ‘perfect’ number is one for which the sum of all its proper divisors (whole number divisors) is equal to the number. Let’s take 6 as an example; it’s divisors are: one, two and three; if we sum them up we have 6! These perfect numbers are quite rare and really cool. The next perfect number is 28, which has the following divisors: 1, 2, 4,7,14; summing them up we have 28! And so on.. The next perfect number would be 496, and after that it’s 8128.

I’ll come back tomorrow with more neat numbers! Cheers!

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Algebra, Analysis, General, Geometry

The Language of Mathematics

“Mathematics knows no races or geographic boundaries; for mathematics the cultural world is one country.” David Hilbert (1862-1943)

I started studying Maths in Romanian, and I have to admit, I was a very dull kid. Why I say that? Because I didn’t have the mind of a genious, I didn’t have a vision of the world or etc. In time, I’ve come to the conclusion that if you want to know something, you have to know to ask the right questions. And every science man knows that asking question makes the whole algorithm! So I started asking myself what if I want to talk to people about Maths, my parents, friends, colleagues, would I know how to explain it? And what if I wanted to talk to a foreign person, how would I talk to him, would he understand me? Is Math the same for everybody?

Well of course it is, it’s a universal language! The simbols are the same for each country! I bought a book written in English, which was about Pythagoras’ theorem when I was 13 years old, and I just learned about it at school. I understood some words and even some sentences, but it didn’t matter because all I needed was explained to me with symbols I knew how to read from Maths class. During college I had the opportunity to share my knowledge with exchange students, and professors from other countries for whom I held presentations in Analysis and Geometry. I must admit that my English isn’t so fluent as I wished for, but they understood me completely as I did too when they were in my place. That’s the beauty of it!

Amazingly, Maths may be universal in the truest sense of the word. And it is fr this reason that the Search for Extraterrestrial Intelligence uses binary representations of π and prime numbers to broadcast our presence to anyone who might be listening. Why would that be? Maybe because they might talk another language and not understand the word hello, but a circle is a circle for them too, and they would know what π is, and the binary concept would be obvious (on/off, day/night).

So what do you think now? Isn’t it beautiful?  Maths is dynamic and its ever-present nature is its most powerful quality.

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Algebra, Analysis, General, Geometry

A Short History of Mathematics

Textbooks nowadays don’t show kids where Maths has come from, or when it was discovered. In my opinion Maths or any other part of the Science field was here long before humans can decipher it. It has been shown that crows can distinguish between sets of up to four elements, a fact that demonstrates that counting occurs in other creatures. Maths has a very long history, not very known by many, and though I had a passion for it all my life, I only read about it’s history during college. And not even then, it’s roots were so clear to me. And after reading some books I could only draw the conclusion that if you want to study the history of maths, you have to study the history of civilization. Although many important results of mathematics go way back to Renaissance, we have to wonder what made them possible? Who decided which language to use, what simbols to use as numbers, or what were the numbers by the way ? Fibonacci was the one who introduced Hindu-Arabic numerals to Europe in the thirteenth century, and freed the mathematicians from the constraints of Roman numerals. ancient math So basically, Maths has been developed everywhere in the world, but the speed of it’s advance was not the same for each region. Ideas have been discovered and lost, and then refound. The modern mathematics borrows ideas from many different places, but the combination between Arabic and Persian Maths with the Greek and Indian gives what we learn today. Though it was discovered in different times in different parts of the world, the results were basically the same, and thanks to the Renaissance mathematicians we have the results that everybody uses now.

Maths hasn’t been so developed at it’s beginning, obviously, but it raised many interesting questions, and gave freedom to think. Nowadays, Maths results are rarely given, but it became used in many other new fields as Computer Science. But you don’t have to be a computer whiz or a math genius to appreciate the beauty of numbers. You don’t have to understand the equation that stands behind everyday things, you only have to become more aware of Mathematics’ influence in the world around you.

And as the great Rene Descartes said, “With me everything turns into mathematics”, make it possible with you and the world will be bigger, more meaningful and more beautiful.

 

photo from: http://graphics8.nytimes.com

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Algebra, Analysis, General, Geometry

An Introduction.

Words have never come easy for me, they only made sense when I’ve read them written by someone else. This is one of the reasons I’ve been attracted to Science. Unfortunately Science covers a wide range of subjects such as Physics, Chemistry and many others related to them. I’m an Aries, so obviously I wanted to top all those classes, and I did, but couldn’t discover them in depth. So I focused on studying the language that connects all the Science fields: Maths. One can study Physics/Chemistry all his life, but without this irreplaceable tool you get nowhere. Even Einstein had the help of Max Planck (well-known german physicist) when he developed the Relativity Theory, because it was known that Maths wasn’t one of his strenghts.

Mathematics means many things to many people. Most see it as a daunting subject, whether you try to solve an ecuation or add up the bills, almost every time you end up with a headache. But for the others it represents the beauty of the universe. An English Matematician and philosopher, described it as “the most original creation of the human spirit”.

Maths has been described in many ways: the science of numbers and magnitude, the science of patterns and relationships or the language of science. Galileo claimed that “The Laws of Nature are written in the language of mathematics”. Very very true! Just by seeing the award winning movie “A Beautiful Mind”, we can see how Maths apply in the day-to-day activities. Unfortunately, neither the media or the books cover the most important part of it: it’s root, it’s history, the place it came from! I’ve been asked more than once by my pupils who discovered the numbers and the operations, and I was ashamed to admit that I didn’t have a clue, no one ever told me and I didn’t even ask myself. So my future posts will come to help your curiosities and maybe widen your horizons. Cheers 😉

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