Diophantus Epitaph
An epitaph is a short text honoring a deceased person. The Greek father of algebra, Diophantus of Alexandria born sometime between AD 200 - 214, and died aged 84 sometime between AD 285 - 299. The puzzle implies that Diophantus lived to be 84 years old. However, the accuracy of the information cannot be independently confirmed. One of the problems (sometimes called his epitaph) states: By the same way, as the headstone says Diophantus age, nature says things through the data. We determine first Diophantus age.
'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.'
L/6 of his time life he spent as the boy
L/12 he lived to youth
L/7 he lived before getting married
5 years later born his boy
L/2 was the age of the boy
4 years went before he himself died
L = L/6 + L/12 + L/7 + 5 + L/2 + 4
L = 14L/84 + 7L/84 + 12L/84 + 5 + 42L/84 + 4
=>
L = 75L/84 + 9
3/28 L = 9 => L = 28/3 x 9 = 84 years
His boy was 42 year old when died and Diofantos 84 years. The example shows the way to determine the relative lengths of life and how such a task can be solved. Little is known about the life of Diofantos, but the age is known carved into the stone.
21.6.2018*08:00 (920 - 309)
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