Pyramid request

[Seeking One]

I did a little brainstorming with a quick web search for information that might fill in the gaps here.

Would a PVC pipe frame and canvas walls be adequate for the purpose?

This guy's simple, inexpensive little do-it-yourself project might work:
http://members.cox.net/randwhit/popup/halfling.htm

As might this guy's "two half pyramids":
http://www.equipped.org/tarp-shelters.htm

Building a small Cheops-shaped pyramid:
http://www.ehow.com/how_2246820_build-ka...ramid.html

Calculations automated:
http://www.1728.com/volpyrmd.htm

...

Thanks to everyone for the great references and contributions to this thread so far! I'm planning on doing a little experiment on some seeds before I plant my garden this year, and like GLB, I too don't want some crazy fly-seed half-breed going into the ground!

I've been having a tricky time trying to determine what exactly is the "apex angle" for a *5* sided pyramid. I simply stress *5* because I was making a silly error for a while using the pyramid calculator above (and linked below again) and thinking of 4 "vertical sides" and not considering the base as a side.

Anyway, in trying to figure this out, here's what I've got so far:

Assuming this angle & length pyramid calculator is correct (I haven't broken out my calculator)

http://www.1728.com/volpyrmd.htm

then I want to assert that the "vertex angle" IS NOT the "apex angle" talked about in the Ra material in the referenced posts above when we’re calculating a 5 sided pyramid.



This Wikipedia article gives a little definition for how to visualize an apex angle:

http://en.wikipedia.org/wiki/Solid_angle#Pyramid

"The solid angle of a four-sided right rectangular pyramid with apex angles A and B (dihedral angles measured to the opposite side faces of the pyramid) is..."

Now, this was a little confusing to read at first, but this is actually a pyramid with 5 total sides... a rectangular base and 4 triangle sides (which is what threw me off when trying to use 4 "sides" in the pyramid dimension calculator above).

Anyway, here is how I understand what that means in relation to the graphic used to demonstrate the angles and lengths given by the pyramid calculator above:

The "vertex angle" is simply the angle that a single, triangular face of our pyramid makes at the "top" of our pyramid. So that means it is *not* the “angle measured to the opposite side faces of the pyramid”.

Picture a triangle standing up inside our pyramid which has it’s “top” at our pyramid “top”, and runs down the middle of two opposing pyramid sides, and also has it’s centre of base intersecting our pyramid base centre point. The vertex angle of THAT imaginary triangle is equal to our apex angle. If you “stood up” one side of our pyramid so that is was fully vertical like our imaginary triangle in the middle (right angle to the base), the side triangle from our pyramid would be larger. *My brain tells me* (though I’m not 100% sure) that this means it has to be a different top angle if the base sides of our triangles are equal, which they are because we’ve got a square pyramid base.

For another way to help you picture this, close your eyes to visualize while you read the following.

Label the picture of our pyramid from the calculator giving the front, light blue side “A”, the left, gray side “B”, back side “C” and right side “D”. Now picture a section of triangular tubbing (like a cylinder, or square tubbing, only with triangle ends) inserted through our pyramid (pretend the sides are made out of paper or something) entering via side “A” and exiting via side “C” at the back. Now assume that the height of our triangular tubbing is the same height as our pyramid and it’s slope (“slant”) is the same slope as the sides “B” and “D” that are “resting” on top of the triangular tube we just inserted through sides “A” and “C”. Ok, still have your eyes closed? Good, now picture the end triangle shape of our tubbing, with it’s top “vertex” angle being our actual “apex angle” now. The reason they’re different compared to a triangle side from our pyramid is because “one triangle is slanted and one is standing straight up”.

Geez, I wish I could draw. I hope that has made everything overly complicated for everyone!

So, in conclusion, the way to determine the apex angle is to use the "yellow" slant (aka slope) angle and a little math. Unfortunately, we can't have the calculator "work backwards" from the result angles below, so we must keep tinkering with the "Base Length" and "Height" values to get our desired "slant angle".

From the slant angle, we calculate *half* of our apex angle to be:

180 - 90 - slant angle = 1/2 apex angle

I went with a slant angle of 56 degrees giving me an apex angle of:

180 - 90 - 56 = 34
34 x 2 = 68 degrees

To simplify my measurements, I ended up using
Number of sides: 5
Base Length: 23 (I’m planning on using inches to measure, not feet!
Height: 23

Which gave me a slant angle of 55.5 (close enough), and 30.2 for my Edge Height (much easier for me to just use 30” for this first pyramid of mine... I’m not going to get too fancy with my measuring here)

You could also just go ahead and use the Giza pyramid's 51.8 degree slant angle as a threshold and be sure your slant angle is *greater* than this number, for the safety reasons mentioned in previous posts.

I’m “fairly sure” about all this, but does my logic make sense or am I missing something?

Here was another site that helped me a little:

http://www.ehow.com/way_5467357_homemade-pyramids.html

I’m about to head outside to jerry-rig this thing together using simple lumber and rope (not even worrying about cut angles for now).

I’ll let ya know if I manage to grow a monster! :p

-Ben