Geometry Help

I will try to give you some insights, some geometry help in this elegant mathematical field which is regaining some popularity after the dark ages of the past few decades.

To us today, it seems that geometry is full of drawings, rules, numbers, strange concepts such as symmetry, difficult ideas such as area, surface and volume. Enough to get more than confused and eventually refusing it fully.

In reality, in my opinion, geometry as it was originally thought and practiced by the Greek, was quite simple, at least in the first "chapters".

It had to do more with "how to think" rather than "formulas" and rules. The scope was to think in a well disciplined way and to establish relations (both spatial as well as proportional) between, dots, lines, surfaces.

Euclide (about 300 b.c.), was a maths teacher in Alexandria when he wrote his famous work "The Elements ", but he himself was probably not such a good scholar and simply collected the work of others (e.g. Eudoxe, Theaetetus)..

The Euclidean geometry was done with two simple instruments, straightedge and compass.

That means, no numbers!

The straightedge is a "ruler" without marks, a tool to make a straight line.

You could use a piece of properly cut wood as well.

The compass is not jut a tool to make circle, but also to "hold" identical length of straight lines...

Lines, dots, circles.

That's it!

In order to enter the beauty of greek Geometry try this simple exercise.

On a piece of plain (not squared) paper make a triangle with identical sides (an equilateral triangle, yes) using a straithedge (nor a ruler!) and a compass.

Don't run, play with the idea and enjoy the puzzle.

Do it with love, calm, patience.

It doesn't matter if you can't do it. But honestly try on your own.

A piece of plain white paper, straithedge and compass and a pencil.....and you.

The solution is here .

Do you know how to cut a circle in thirds using only a compass?

Solution

From Geometry Help back to the homepage

Source: Bordas Encyclopédie, Peruzzo ed., 1972