Pythagorean Triangles: what's the big deal

I understand that the Egyptians held these triangles in high regard and that the eye of Horus is in the shape of a pythagorean triangle and that it's a neat thing to do to draw little squares along the triangle's sides. Why has this shape been so sacred over the years?

For a lot of reasons. It's a fascinating structure, and has a lot of applications everywhere in mathematics. If you've ever read Euclid, you'd appreciate this structure.

But that's not the Egyptians. One of the main reasons they would like it is because if you take a string divided into parts 3, 4, and 5 units long (a pythagorean triplet) you can create a perfect right angle.

Useful when you wanna build things.

here's an intersting page on it
www.luckymojo.com...

Then get 3 sticks -- thin ones, just strong enough to stick into soft soil. Stab one stick in the ground and arrange a knot at the stick, stretch three divisions away from it in any direction and insert the second stick in the ground, then place the third stick so that it falls on the knot between the 4-part and the 5-part division. This forces the creation of a 3 : 4 : 5 right triangle. The angle between the 3 units and the 4 units is of necessity a square or right angle.

The ancient Egyptians used the string trick to create right angles when re-measuring their fields after the annual Nile floods washed out boundary markers

Geo Metry, measuring the earth.


Consider that it also permited knowledge of something hidden by using something known, ie, the lengths of the sides to get the angles.

Here is another essay on the subject that looks interesting
www.jwmt.org...

And for more of the masonic connexion:

Mnesarchus[pyhtagoras' father] was said to not to have been Greek, but a Phoenician, originally from the city of Tyre.

Tyre being, of course, the seat of King Hiram and home of Hiram Abif.

Pythagoras also appears in Masonic writtings, but not the earliest ones, as "Peter Gowas", apparenlty an anglicization of a foreign and obtuse name.

I have been reading through a range of articles and websites regarding some pythagorean theory which leads to a range of other fascinating information. One of the websites with some info to read on is:
www.halexandria.org...
or try
www.cs.utk.edu...

. This is my first post so i hope i responded in the proper format etc and that the links came out ok.

if this helps any, in a mason handbook i just happened to come across, it has a part about The Forty-Seventh Problem of Euclid and some statements about how great Pythagoras was and how it teaches Masons "to be general lovers of the arts and sciences."

Originally posted by Amorymeltzer
One of the main reasons they would like it is because if you take a string divided into parts 3, 4, and 5 units long (a pythagorean triplet) you can create a perfect right angle.

Useful when you wanna build things.

Yep.
a² + b² = c²
It's how you make something "square".

Most people don't realize how vital to construction the right angle actually is. Thats what those little squares in the corners of some drawings are that were refered to in the original post. The triangle is also the 1st and simplest geometric structure that is 3 dimentional (point = 1 dimention, line or two points = 2D, triangle or 3 points = 3D).

Thanks for all the replies and links. I haven't gotten to check them out yet but I'm sure it'll be some good stuff.

I'm wondering about this because I most recently ran across some stuff about the 3-4-5 in the following book which touches on Euclid's 47th problem:

The Apron: It's Traditions, History and Secret Significances
by Frank C. Higgins - 1914
Kessinger Publishing
ISBN: 1-56459-418-1

EDIT: I'll try to scan a page in within the next few days.

[edit on 8-11-2005 by 2nd Hand Thoughts]

Originally posted by Ambient Sound
Yep.
a² + b² = c²
It's how you make something "square".

Anyway, I highly suggest reading Euclid's The Elements if you're interested in this stuff, 2nd hand thoughts. It can be slow, but the propositions are fascinating. For example, after reading it, I used the fact that parallelograms on equal bases in the same parallels are equal in my linear algebra class. Book I culminates in his proof of the Pythagorean Theorem, which is, if I do say so myself, über cool. The comments along with each bit are equally interesting, as well.