Comments on: Phi and Geometry

By: MICHAEL J STEFANO

MICHAEL J STEFANO — Wed, 06 Mar 2024 14:26:00 +0000

5. IMPORTANT TO INDICATE THAT IT MUST BE A REGULAR PENTAGON (EQUAL SIDES), JUST LIKE THE TRIANGLE EXPLANATION NOTES THAT IT IS AN EQUILATERAL TRIANGLE. THE SQUARE EXAMPLE IS SELF-EXPLANATORY BECAUSE OF THE DEFINITON OF A SQUARE AS A QUADRANGLE WITH EQUAL SIDES AND EQUAL ANGLES, BUT THIS MUST BE SPECIFIED FOR TRIANGLES AND PENTAGONS.

By: Prajna

Prajna — Fri, 18 Aug 2023 14:20:19 +0000

In reply to Gary B Meisner. A triangle with base = height is iscoceles rather than equilateral but such a triagle, where the base=height has an inner radius of 1/phi * base/2. In other words, the inner radius is the phi mean of half the base.

By: Prajna

Prajna — Wed, 16 Aug 2023 16:38:31 +0000

In reply to Gary B Meisner. Sorry, there was a mistake in my previous comment. The inner radius is down from the apex by the length of the side (which is ths sqrt of 5 times half the base) times phi minus 1. If you bisect the side a line perpendicular to the side meets the meridian of the triangle at the centre of the inner circle.

By: Prajna

Prajna — Wed, 16 Aug 2023 15:53:37 +0000

In reply to Gary B Meisner. Well actually, phi can be derived from such a triangle (it is really an isosceles triangle with base = height.) Half the side (square root of 5 times half the base) gives the circum radius. A line perpendicular to the side one circum radius from the apex meets the meridian of the triangle at the centre of the inner radius. The inner radius is the golden ratio mean of half the base.

By: Gary B Meisner

Gary B Meisner — Sat, 20 Aug 2022 16:07:56 +0000

In reply to X3N0N9. Thanks. You're very welcome. See the About page for more about the existence of this domain. Regards, Gary Meisner

By: X3N0N9

X3N0N9 — Sat, 23 Jul 2022 18:34:17 +0000

This stuff, the whole hekin page. Absolute fire like totally tetrahedron stuff. Actually after writing that I came to a thought that this is more like Aether level stuff, infinite brilliance the dodecahedron. Thank you for all who are responsible of existence of this domain.

By: Vdj*

Vdj* — Mon, 02 May 2022 17:41:42 +0000

*dreams with the time you find out the answer *

By: Vdj

Vdj — Mon, 02 May 2022 17:38:10 +0000

In reply to Dianne Power. *polar star*

By: Gary B Meisner

Gary B Meisner — Wed, 26 Jan 2022 14:01:23 +0000

In reply to Khalfan Aziz. Good thought, but that approach only provides some elements related to the golden ratio, but doesn't provide a construction showing the golden ratio itself.

By: Khalfan Aziz

Khalfan Aziz — Sat, 15 Jan 2022 17:44:46 +0000

My simplest method is the equilateral triangle of base 1 unit and height of 1 unit.
Then 1/2 base plus the slant is Phi.
The slant is (1/2) times root 5