Measurement tool?


In my case it's operator error. I started with a subdivided cube,
when I should have just linear subdivided after the fact.
 
* Frank B has therefore proven that the ancient Pythagorean rule is (not quite) correct. I am both surprised but also a bit sceptical :confused:
 

We used 3',4',5' or 6',8',10' for marking accurate 90
degree layout lines with a tape measure pre building walls.

 
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* @ Pythagoras:
* The Pythagorean rule does work on right angled triangles. As a matter of fact it only works for right angled triangles.
* An equilateral triangle has three angles of 60° each, so Pythagoras does not apply.

* As by your own example:
* a^2 + b^2 = c°2 => 3^2 + 4°2 = 5^2 => 9 + 16 = 25
* Please correct your misleading statement on this matter.

* By the way, there are equilateral right angled triangles on a sphere, where all three angles, alpha, beta and gamma, are 90°. There does exist a spherical Pythagorean theorem, cos(c/r) = cos(a/r) cos(b/r).
* a, b and c are the sides, r is the radius.
 

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* @ Pythagoras:
* The Pythagorean rule does work on right angled triangles. As a matter of fact it only works for right angled triangles.
* An equilateral triangle has three angles of 60° each, so Pythagoras does not apply.

* As by your own example:
* a^2 + b^2 = c°2 => 3^2 + 4°2 = 5^2 => 9 + 16 = 25
* Please correct your misleading statement on this matter.

* By the way, there are equilateral right angled triangles on a sphere, where all three angles, alpha, beta and gamma, are 90°. There does exist a spherical Pythagorean theorem, cos(c/r) = cos(a/r) cos(b/r).
* a, b and c are the sides, r is the radius.

I bet it doesn't work on a Right Isosceles Triangle :tongue:
It must be a Pythagorean triple.

 
* A simple right angled isosceles triangle would be a = b= 1 and c = square root of 2. Pythagoras does apply, as expected :tongue:
 

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* Oddly enough, in 2nd-ary schooling (in Europe about 11-18 years of age) I was a dimwit in mathematis (plus physics and chemistry). Suddenly, in university, I discovered that this was plain (but not necessarily simple) logics.
* It is still a puzzle what caused this paradigm shift of my cognition.
* It is not the only paradigm shift. Some I welcome, some I regret.
* Well, back to square 64 :rolleyes: :tongue: :confused:
 
* Thank you.
* It is a pleasure to communicate with somebody who seems to be a human / humane being. I thought you folks were on the verge of extinction :mrgreen:

* Addendum:
* Of course, this is not math (US) / maths (UK) but advanced counting on 10 fingers. Pythagoras has been dead for 2.5 millennia.
 
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Phi: The Golden Mean

(Interesting thread timeline, from 2005 — 2016 — 2018, from point-to-point distance to non-Euclidian triangles.)

People who like C3D like geometry.

This thread's topic of a pyramid's angles reminds me of two personal obsessions: the Great Pyramid and the ratio of Phi. The attached images depict the incorporation of Phi as a primary feature of the Great Pyramid, and a C3D "ruler" I made to facilitate the incorporation of Phi in one of my own designs.

Should I get a commission to design another Pyramid, I'm good to go.

If you are unfamiliar with either the Great Pyramid or Phi, consult the Internet to discover them. You will be astonished at their geometric perfection and significance, in mathematics, art and architecture, and throughout nature. Phi is as universal as Pi, yet relatively unknown.

From its completion around 2560 BC until 1356 AD the Great Pyramid was almost mirror-smooth and perfectly geometrical, a monument to the knowledge of the Egyptians. Then outer casing stones were removed to provide the materials for a mosque in nearby Cairo, hence the irregular stepped appearance of today.

1.618 : 1 = 1 : .618
 

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around 2560 BC until 1356 AD the Great Pyramid was almost mirror-smooth and perfectly geometrical

A lot is written about pyramids, about their perfection an so on. And mostly it's, well, a bit exaggerated from the historians of the old. Nobody knows how smooth the pyramid would have been to our modern eyes, neither in 2560 bc nor in the middle ages ...


That aside, a general tip for those who want to create things but don't like geometry that much. Like me. I remember some of Pythagoras formulas quiet well, but honestly I have forgotten the most of what I ever had to learn in that aspect.

In this relatively simple case, frank's example is what works best. But sometimes, when you need an angle or a height ... Just use simple background geometry (the simpler the better). In Cheetah you have to do it often by eye, as snapping is not always possible, but in the flat views (i.e. top, front, left etc.) with wireframe and zooming in you usually get near enough (45° = easy with half a square poly). With subdiv it's sometimes the only possibility (it 'd be a bit a lot of math to account for catmull-clarke also while calculating your object ...).

In a few cases I stick together the raw form of an object together with a few primitives (just the outline for example) so I have something that gives me visual orientation if I can't use a background image (or to create one would be to much trouble).
 
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