Real Numbers

The beginnings.

Complete the text with the following words

Rational numbers

Powers and roots

Real numbers

There are different kinds of numbers; first you have studied whole numbers and integers, with them you can add, multiply and subtract. After that you studied rational numbers, and division became possible.

But there are other operations that cannot always be done with rational numbers. 

Can you calculate the square root of 3 obtaining a rational number? No, you can’t, so you need new “friends”!

You will recognize these new numbers because they have infinite decimal figures…which do NOT repeat!

These numbers were called “a logos” (or “with no sense” in Latin), now they are called irrational numbers.Rational and irrational numbers are separated sets of numbers, and together they form a bigger set, the set of the real numbers.


Pythagoras was an ancient Greek philosopher and mathematician. He was born on the island of Samos (570 BC.). He traveled widely when he was young and he went to Egypt and other places searching for more and more new things to learn. Around 530 BC he moved to Croton (Greece) and founded a religious sect. His followers were convinced that “numbers are everything”. They believed that numbers represented magical things, it was a religion. They studied numbers deeply, doing interesting classifications, discovering important things about them. Their investigations are very important even today. You surely remember the famous Pythagoras theorem (he was not the one who discovered it but he studied it deeply).

The square roots of 2, 3, 5, 6, …, etc are the first irrationals that we can think of. Pythagoras was really worried about the square root of 2. He forbidden the members of the Pythagorean order to talk about it. 


We identify Pi with the greek letter π (Pi) and is a number well known since the beginning of civilization.

  represents the relationship between the length of a circumference and its diameter. 

The ancient Egyptians already knew about this relationship. They assigned the value {"font":{"color":"#000000","size":11,"family":"Verdana"},"backgroundColorModified":false,"code":"$$\\frac{256}{81}$$","backgroundColor":"#ffffff","id":"1","aid":null,"type":"$$","ts":1647020218467,"cs":"rrfe9RDL+MbuCgAX6c9scw==","size":{"width":29,"height":36}}

The Babylonians also knew this number and assigned the value {"backgroundColorModified":false,"backgroundColor":"#ffffff","type":"$$","aid":null,"id":"2","code":"$$3\\,+\\,\\frac{1}{8}$$","font":{"family":"Verdana","size":11,"color":"#000000"},"ts":1647020235956,"cs":"1kLn947SrhAExEaCRNE05A==","size":{"width":50,"height":36}}.

The Greeks came a little closer and used the value {"aid":null,"font":{"size":11,"family":"Verdana","color":"#000000"},"backgroundColorModified":false,"code":"$$\\frac{377}{120}$$","type":"$$","backgroundColor":"#ffffff","id":"3","ts":1647020260827,"cs":"KVMqWYu5ifWh0sqJOtfr+w==","size":{"width":29,"height":36}}.

In China an attempt was also made to give an approximation for  π, Tsu Ch’ung Chi in the 5th century assigned the value {"backgroundColorModified":false,"font":{"size":11,"color":"#000000","family":"Verdana"},"aid":null,"type":"$$","backgroundColor":"#ffffff","id":"4","code":"$$\\frac{355}{113}$$","ts":1647020281740,"cs":"eF6/qTMai9MZ8NzXXGOLpg==","size":{"width":29,"height":36}}.

Pi Letter Soup

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