Tuesday, June 30, 2009

The Heptadecagon

Considering I have not yet found the one to feature today, I will post an article about the so-called "heptadecagon". I translated it from Chinese and added a little bit of my imagination. Read on, you will find out what it is.

P.s. I am unable to upload any picture for the moment, will do it later.

Best of love,
The Heptadecagon

Photo Credit: La.Joie.de.Vivre

One day in 1796. University of Gottingen, Germany.

A young man started working on his homework after dinner: considering his extraordinary talents in maths, his tutor left him 3 maths problems each day as homework.

The first two problems were soon solved- they took no more than two hours. The third one was written on another piece of paper: Construct a regular heptadecagon by compass and straightedge.

It was a tough one. The young man found what he had learned did not help much to make the problem any easier. Time is ticking out and no progress was made.

The frustration, however, made the young man think harder for some unconventional perspectives and solutions. He said to himself that he could devise the construction in the end and he would.

He did it, at the dawn of the next day.

When he met his tutor, he said with regrets,"It took me the whole night to solve the third one- I should have done it better..."

The tutor was astonished after checking out his student's homework, his voice trembling,"And you reached the solution all by yourself?"

"Yes, all by myself." the young man was a bit confused by the question.

Stretched a piece of blank paper on his table, the tutor asked his student to take a seat, and to construct a regular heptadecagon, using only a ruler and a compass. He wanted to see with his own eyes how this young man could do it.

Amazed by the fact that the young man completed the work within a short time, the tutor said excitedly,"You know what? This problem, a mystery, has occupied the mathematicians since the days of Ancient Greeks! Archimedes did not find out the way-out, nor did Newton! But finally you made it! You put an end to this mystery, within a night! You are really a prodigy!"

The tutor himself had been trying hard for a solution, too, and that piece of paper with that problem was given to the student by mistake...

When looking back at this legendary experience, the young man always said,"If anybody had told me that the problem had been an unsolved mystery for over 2000 years, I would have no faith to work it out."

This young man was later known as the Prince of Math, Carl Friedrich Gauss (1777- 1855).

Photo From: http://www.chops.com/

It is not because things are difficult that we do not dare; it is because we do not dare that things are difficult.

In geometry, a heptadecagon is a 17-sided polygon ("hepta" means "7"; "deca" means "10"). So pleased by the discovery of the construction, Gauss requested that a regular heptadecagon be inscribed on his tombstone. But the stonemason declined, claiming that the difficult construction would essentially look like a circle- so it was later decided that a star would be used on a monument honoring him instead.


Al said...

thats an inspiring story :)

Fran said...

Glad you liked it Al!

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