04-12-2012, 12:27 PM
(This post was last modified: 04-12-2012, 12:51 PM by Steppingfeet.)
51/49, finally had some time to sit down with your pyramid post today, and I'm happy to report that with your aid I've made some breakthroughs in moving closer to creating an equilateral pyramid with a square base.
Let's begin.
You used this link to determine the angle of your cuts:
http://www.1728.org/volpyrmd.htm.
(The description says that "The diagram... depicts a right regular pyramid - a solid geometric figure whose base is a regular polygon , whose faces are all congruent isosceles triangles, and whose vertex is perpendicular to the center of base." This matches the definition of an equilateral pyramid on a square base as well, as equilaterals are a type of isosceles triangles, I've learned.)
The calculator asks for three inputs:
1) number of sides
2) height of apex
3) base length.
I could determine 1, obviously four sides, and 3, which I arbitrarily set at 72 inches (6 feet), but didn't know what the height of an equilateral pyramid would be.
So I found this formula for determining the height of an equilateral pyramid using the length of any one side, "a":
Formula.png (Size: 538 bytes / Downloads: 183)
(If this image isn't coming through, the formula is: Height equals 1 over the square root of 2 times "a".)
Using the formula, I was able to determine that an equilateral pyramid with a base length of 72" has a height of 50.91". Subsequently I could enter in the three needed inputs to determine angle cuts!
After entering the three inputs, both the "vertex angle" and the "base angle face" come out to 60 degrees! As they should in an equilateral where all three interior angles are 60 degrees and, as with all triangles, total 180 degrees.
But I've known all along that the interior angles should be sixty degrees. I just haven't known how to cut the wood to achieve that specification, especially considering that all four of the triangles lean inward to meet above the center of the base.
How were you able to determine at what angle to cut the wood in order to produce your desired specifications? Does one of the fields in the pyramid calculator indicate that?
And how do you make the apex cuts so that they come together to form the apex? The ends of each piece of wood would need two cuts in order to conjoin with the pieces to its left and right.
I won't reach for NASA-level precision in achieving interior angles of 60.00001 degrees, but I want to get as close as possible.
Any help that you or any other can give would be much appreciated! Just figuring out how to cut the wood pieces to accurately form an equilateral pyramid is most of the battle for me. The only other remain question after that is how best to fit them together.
With love, GLB
PS: If you were interested in knowing, Ra advised against using base metals in the construction of a meditation pyramid.
Copper (the material you've used to secure your pieces together) is a base metal it seems: http://en.wikipedia.org/wiki/Metal#Base_metal.
Let's begin.
You used this link to determine the angle of your cuts:
http://www.1728.org/volpyrmd.htm.
(The description says that "The diagram... depicts a right regular pyramid - a solid geometric figure whose base is a regular polygon , whose faces are all congruent isosceles triangles, and whose vertex is perpendicular to the center of base." This matches the definition of an equilateral pyramid on a square base as well, as equilaterals are a type of isosceles triangles, I've learned.)
The calculator asks for three inputs:
1) number of sides
2) height of apex
3) base length.
I could determine 1, obviously four sides, and 3, which I arbitrarily set at 72 inches (6 feet), but didn't know what the height of an equilateral pyramid would be.
So I found this formula for determining the height of an equilateral pyramid using the length of any one side, "a":
Formula.png (Size: 538 bytes / Downloads: 183)
(If this image isn't coming through, the formula is: Height equals 1 over the square root of 2 times "a".)
Using the formula, I was able to determine that an equilateral pyramid with a base length of 72" has a height of 50.91". Subsequently I could enter in the three needed inputs to determine angle cuts!
After entering the three inputs, both the "vertex angle" and the "base angle face" come out to 60 degrees! As they should in an equilateral where all three interior angles are 60 degrees and, as with all triangles, total 180 degrees.
But I've known all along that the interior angles should be sixty degrees. I just haven't known how to cut the wood to achieve that specification, especially considering that all four of the triangles lean inward to meet above the center of the base.
How were you able to determine at what angle to cut the wood in order to produce your desired specifications? Does one of the fields in the pyramid calculator indicate that?
And how do you make the apex cuts so that they come together to form the apex? The ends of each piece of wood would need two cuts in order to conjoin with the pieces to its left and right.
I won't reach for NASA-level precision in achieving interior angles of 60.00001 degrees, but I want to get as close as possible.
Any help that you or any other can give would be much appreciated! Just figuring out how to cut the wood pieces to accurately form an equilateral pyramid is most of the battle for me. The only other remain question after that is how best to fit them together.
With love, GLB
PS: If you were interested in knowing, Ra advised against using base metals in the construction of a meditation pyramid.
Copper (the material you've used to secure your pieces together) is a base metal it seems: http://en.wikipedia.org/wiki/Metal#Base_metal.
Explanation by the tongue makes most things clear, but love unexplained is clearer. - Rumi