Any maths buffs?

Posted on Sun 3rd, January 2010

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• #426

NotThamesWater in reply to @Greenbank

Obligate spheroids. They have little choice.
• #427

moocher
Apologies for the technical drawing

I want to make an 8 sided cone, sitting inside a circle of R with a height of H

What dimensions (base and length) will each of the composite triangles need to have?

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• #428

Greenbank

The long length (of each piece) is simply a right angle triangle with sides R and H.

L = sqrt( R² + H²)

For the length B think of the top down view, you have an isoceles triangle with an internal angle 45^o and two sides of length R.

You can split this up into two right angled triangles with hypoteneuse length R and opposite angle 22.5^o.

sin 22.5 = opp / hyp

opp = R * sin 22.5

So half B would be 0.38268 (5dp) * R

So B would be 0.76537 (5dp) * R
• #429

moocher

Thanks. I'll need to read it very slowly and carefully. Then make a little excel calculator
• #430

Brun
I figured there must be a formula for B based on radius and number of sides. Google led me to this...

Edit: Since that's the perimeter and you only want one side, I guess it starts '2r sin...'

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