Cryptography by team F

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India and the zero

The concept of zero as a number and not merely a symbol or an empty space for separation is attributed to India, where, by the 9th century AD, practical calculations were carried out using zero, which was treated like any other number, even in case of division. (source: Wikipedia)

Ché Guevara – Fidel Castro: One-time pad cipher

Ché Guevara used a number code when communicating with Fidel Castro. He transposed each letter in the text to a number […]. He then wrote those numbers one behind the other. Below that line he wrote a second line of numbers, known only to him and Castro, which was used only once. He then added both lines, number per number, and below each set of numbers he wrote (the last digit of) the sum. This give a third line of numbers. Only that row was transmitted. When Castro subtracted the second line from the third, he had the first line as the result.

The Ché method cannot be cracked because the key (the second line of numbers) is random, as long as the message, is only used once.

(source: https://themathematicaltourist.wordpress.com/page/2/)

Here is a photo of the original manuscript:

More details: http://serdis.dis.ulpgc.es/~ii-cript/PAGINA%20WEB%20CLASICA/CRIPTPLOGIA/CIFRADO%20ONE-TIME%20PAD.htm (in Spanish)

The Zero

·Several ancient and great civilizations, such as Ancient Egypt, Babylon, ancient Greece have documents showing mathematical character symbols
indicative of zero.

· The nfr sign to indicate zero was used in ancient Egypt.

· The Mayans were the first to devise zero.

numeracion_maya

Andrew Wiles and the proof

-Sir Andrew John Wiles KBE FRS (n. Cambridge, England, April 11, 1953) is a British mathematician.

-It reached world reputation in 1993 for exposing the demonstration of Fermat’s last theorem, which though in this opportunity it turned out to be unsuccessful, finally managed to complete it correctly in 1995.

-Wiles could demonstrate Fermat’s Last theorem from the connection outlined by Frey, and demonstrated by Ken Ribet in 1985

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Fermat’s last theorem

In number theory, Fermat’s Last Theorem states that no three positive integers a,b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two.

This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians.

enigma was the name of a machine that had a rotating mecanismo encyption and decrypt use both encryption and decrypt messages paw

his cipher that contained the message is supposedly protected causes cosidered have concluded WWII

 

THE TABLET PLIMPTON 322

-Plimpton 322 is a Babylonian clay tablet.

-This tablet is believed to have been written around 1800 BC.

-It is composed by four columns and 15 rows numbers.

-This table shows what now is called Pythagorean triples integers a, b, c satisfying a2+ b2=c2.

 

Plimpton 322

Ready for your ultimate post

After the comments of today, you have to write a new post with more information and the images that will appear in your final panel.

Tips:

  • Try to follow the points of the “list of topics”. You can select some of them.
  • Use short sentences.
  • Put interesting photos and explain them.

Deadline: Monday 24th November 2014

The Zero

• Zero appeared for the first time in Babylon in the third century C.

• Zero (0) is the sign of number zero.

• If you are located to the right of an integer, double value;

The placement of the left unmodified.

cero

Pythagoras Theorem.

pitagoras

·The Pythagorean Theorem states that in any rigth triangle, the square of the hypotenuse (The longest side of a right triangle ) is equal  to the sum of the squares of the legs ( the two shorter sides of the triangle, which make a right anlge).

·Pitágoras de Samos  ca. 569. BC – ca. 475. C.1) was a Greek philosopher and mathematician considered the first pure mathematician.

·Theorem estimated demonstrated by similar triangles: counterparts sides are proportional.
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Numerical system

·Binary system of numeration

-The binary system of numeration uses only two digits, 0 and the 1.

-The value of each position is that of a base power 2, raised up to an equal exponent

to the position of the digit less one.

 

numeros binarios

 

The tablet of Plimpton 322

Plimpton 322Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has the number 322 in the GA Plimpton Collection at the University of Columbia.1 this tablet is believed to have been written around 1800 BC, has a table of four columns and 15 rows numbers.This table shows what now called Pythagorean triples integers a, b, c satisfying a ^ 2 + b ^ 2 = c ^ 2.

Let’s start!

Now you have got a topic, you must start the work. The first thing I want you to do is to write a post with a picture and a brief explanation of it. Obviously, it must be related with your topic.

For example, let’s imagine that I’m working on the topic “Fractals”.  Then, I would post something like this:


  • A fractal is a mathematical object that exhibits a repeating pattern that displays at every scale.
  • Fractals can be seen in Nature.
  • For example, have a look at this Romanesco broccoli. Each of the smaller buds is made up of even smaller buds.

broccoli-1


Deadline: Monday 17th November 2014

Teams and topics

Here are the topics for each team:

  • Team A: Fermat’s last theorem (*)
  • Team B: Numerical Systems
  • Team C: The Tablet Plimpton 322
  • Team D: Pythagoras’ Theorem
  • Team E: Zero (**)
  • Team F: Cryptography

(*) You should have posted something.

(**) Team F was faster than you and they also chose the topic of Cryptography.

Guide to write a post

  1. Click on the Log in link (at the left of the page) (*)
  2. Fill in with your username and password (*)
  3. Click on the Posts menu (at the left of the page) and then click on the Add New link
  4. Enter the title and the text of your post. You can add photos with the Add Media button
  5. Click on the blue Publish button (at the right of the page)

fractal

(*) If you are logged in in your computer (because you stay logged in since the last time), you can avoid these first two steps: just click on the New Post link (at the top right of the page).