Shop Math

[Bruce Cohen]

And I always thought that an elipse was when the moon blotted out the sun and daytime turned to night.

Bruce

[ted van halen]

What is wrong with you people talking about curves not being straight. Everybody knows that a curve is a slightly bent straight line. It can't get simpler than that.

Actually a line is just a straight curve. According to my modelling software.

[Wood_workur]

I'm going to have to ask you to move your discussin about line being curves and what not to a line forum.

[linear]

I have been wanting to build an icosahedron for along time. It is a regular solid with 20 sides, each an equilateral triangle. The SMT makes it easy to whip out triangles, just set the fence to the 30 degree mark. But I never could crack the bevel angle. Today I was looking for something else and found a spreadsheet I did a few years back that found all the face angles for a square-based pyramid (another possible project) and it reminded me where to look for the answer.

http://mathforum.org/dr.math/faq/for...olyhedron.html

Specifically:
delta = arccos(-sqrt[5]/3) = 138.1896851° (roughly ) gives you the dihedral face angle.

So the table saw bevel angle would come out to (180 - 138.1896851)/2 = 20.90515745°.

No one has a protractor that precise, so the usual method is to make a template by constructing a right triangle. With one angle set to 20.90515745°, the ratio of opposite to adjacent sides is tan(20.90515745&#176 = 0.382.

So you draw a 1000mm line, and a perpendicular 382mm line, then draw the hypotenuse of that triangle on a piece of mat board or something similar that's suitable for templates. You cut that out (although you really just need the end opposite the 20.90515745° angle) and use it as a gauge to set your bevel angle. (I may just use my sliding T-bevel) No protractor required, yet it's more than precise enough.

Anyhow, I have a pile of plywood scrap that's earmarked to finding out whether the above is enough to get me to a reasonable icosahedron.

[ted van halen]

I'm going to have to ask you to move your discussin about line being curves and what not to a line forum.

Sorry, didn't mean to hi-jack. Moving on.


Ted