## Lesson 7: Who Was Diophantus? Diophantus’s Riddle (IV)

February 25, 2012**Diophantus of Alexandria**

### Born: about 200 Died: about 284

**Diophantus **is often known as the ‘father of algebra’,but there is no doubt that many of the methods for solving linear and quadratic equations go back to Babylonian mathematics. Nevertheless, his remarkable, collection of problems is a singular achievement that was not fully appreciated and further developed until much later.

He is best known for his Arithmetica, a work on the solution of algebraic equations and on the theory of numbers. The *Arithmetica* is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. The method for solving the latter is now known as Diophantine analysis. Only six of the original 13 books were thought to have survived and it was also thought that the others must have been lost quite soon after they were written. **Diophantus was the first Greek mathematician who recognized fractions as numbers**; thus he allowed **positive rational numbers** **for the coefficients and solutions.**

Diophantus did not use sophisticated algebraic notation, he did introduce an algebraic symbolism that used an abbreviation for the unknown and for the powers of the unknown.

However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived.

You can read a good biography on

http://www.gap-system.org/~history/Biographies/Diophantus.html,

where I found this information. There are many biographies of famous mathematicians.

### **Diophantus Riddle**

** **Much of our knowledge of the life of Diophantus is derived from a 5th century Greek anthology of number games and strategy puzzles. One of the problems (sometimes called his epitaph) states:

**‘Here lies Diophantus,’ the wonder behold.**

**Through art algebraic, the stone tells how old:**

**‘God gave him his boyhood one-sixth of his life,**

**One twelfth more as youth while whiskers grew rife;**

**And then yet one-seventh ere marriage begun;**

**In five years there came a bouncing new son.**

**Alas, the dear child of master and sage**

**After attaining half the measure of his father’s life chill fate took him.**

**After consoling his fate by the science of numbers for four years, he ended his life.’**

** **

This puzzle implies that Diophantus lived …..Could you tell it to us?

### You will publish a post with your solution on this blog and there is an interesting reward for you!

However, the accuracy of the information cannot be independently confirmed.

To Lydia Ascacíbar Rodríguez who left a comment in the wrong place (the presentation page) . Your solution was:

1/6 + 1/12 + 1/7 + 1/2 + 5 + 4= 14 +7 +12 + 42 +5 + 4= 84

We find the least como multiple for eliminate the denominators.

And he was 84 years old when he died.

I can’t see why you give this answer clearly. Probably you are using pre-algebra. If you set an equation you will get the same solution. Youare ading fracions OF THE AGE OF DIOPHATUS , X, YOU DON’T KNOW.

by mongarcia March 17, 2012 at 3:20 pm