I'm building some walnut bedside tables with 24" circular tops. For visual interest...and because it'll be fun... I'd like to use 12 alternating maple and walnut angled segments in a sun burst pattern. Ive gotten far enough to understand that the angles need to be 30°...I think. Do I cut each angle side at 15° ? 

Please help a mathematically challenged old man. And, muchas gracias!!!

 

 

I'm a mechanic not a Professor of Mathematics.

 

You have a better chance if me explaining women than getting some math done.

Edited May 8, 20205 yr by Gunny

If you do the math it's 360/12=30

but  a 4 sided box would be 360/4=90 but we know you have to cut the corners at 45, so yes you would have to cut the angles at 15

360/4=90/2=45

360/12=30/2=15

@Wichman3 and @lew Many thanks !! 

...Maple, and Walnut Pizza!! 

Just remember if you cut a board at 0 degrees on the scale, it's really a 90 degree cut.   It should be obvious at this angle, but if you are doing something like 42 degrees, it's really easy to mess up.

You can make the first cut at 15, then the next one at 30, change the orientation for every cut, and keep cutting at 30.   WW -- gives you 7 pieces if you have wide enough board to get them all out.
 

Unless you are making this of veneer, I'd be fearful that with seasonal expansion/contraction, it's going to blow apart, the top is not going to expand and contract across the diameter (along the grain, board length), but will around the circumference (across the grain, board width).  Or vice-versa, depending upon how you orient the grain.  C= pi* D   (D does not change, C does)

Keith Mealy,  BS and MS degrees in math.

A friend gave me a math theorem to prove last week, that he got from a son working on his PhD in math.  I got stuck on it, but eventually found a counter-example to show that it was not true.   He said, no, it was true.   Unfortunately, he left out one important word that determined whether it was true or false.

Prove:
The sum of two prime numbers has at least three factors.

He forgot to say consecutive prime numbers.

Edited May 8, 20205 yr by kmealy

I'm out!  

13 minutes ago, lew said:

I'm out!  

Assume p and q are consecutive primes greater than 2.
 

That means both of them are odd, so the sum is even.   That makes 2 one factor.
The remainder is (p+q)/2  Since they are consecutive (meaning they are different) that factor is between p and q, and thus must be composite (not a prime)

Counterexample (proving it not true) if you omit the consecutive word.
 

17+5 = 22        17 and 5 are both primes.

one factor is 2, the other is 11.  Both are primes, so it does not have three factors, only two.

Also, if you omit "consecutive" you can say
5+5 = 10 = 2 * 5   so it, too only has two prime factors.

Edited May 8, 20205 yr by kmealy

SHEEEIT looks like another hobby I’m not smart enough for  

 

...It's been awhile...1,2, & 3.

 

 

 

Edited May 8, 20205 yr by Larry Buskirk

Oops! 

1 hour ago, kmealy said:

Assume p and q are consecutive primes greater than 2.

2, 3, & 5...(3 + 5)/2=4 

Edited May 8, 20205 yr by Larry Buskirk

20 minutes ago, Larry Buskirk said:

Oops! 

2, 3, & 5...(3 + 5)/2=4 

8 = 2* 2 * 2   (three prime factors)

1 minute ago, kmealy said:

8 = 2* 2 * 2   (three prime factors)

...Same prime number not greater than 2, and a different formula. 

1 hour ago, kmealy said:

Assume p and q are consecutive primes greater than 2.
 

That means both of them are odd, so the sum is even.   That makes 2 one factor.
The remainder is (p+q)/2  Since they are consecutive (meaning they are different) that factor is between p and q, and thus must be composite (not a prime)

...The way I read the above is 2 is a given, you have to solve for p + q and end up with a factor that is between p + q. 3, & 5 are consecutive primes greater than 2 so (3 + 5)/2 = 4 which is between 3, & 5. 

Edited May 8, 20205 yr by Larry Buskirk

Oh Duh!!! 

Missed that!

3 hours ago, kmealy said:

Prove:
The sum of two prime numbers has at least three factors.

3 + 5 = 8 = 2 x 2 x 2 

 

Edited May 9, 20205 yr by Larry Buskirk

@kmealy, Thanks for the reply. I'll be using the Microjig Mico dial thingie. Not the miter gauge. It can be adjusted to within 1/2 of a degree. 

Here's a picture. 

The tables won't leave Tucson anytime soon. Plus, they'll be in a climate controlled environment. And, the tops will be finished on both sides with oil based poly....or, sealed up with Total Boat's penetrating epoxy. TBD. 

 

3 hours ago, kmealy said:

Prove:
The sum of two prime numbers has at least three factors.

...Just had to jog some old brain cells didn't you? 

13 + 17 = 30 = 2 x 3 x 5 (the sum of two consecutive prime numbers with three consecutive prime factors)

 

I'll quit now that my head hurts! 

Let us see progress and final pictures, @Gene Howe

3 minutes ago, kmealy said:

Let us see progress and final pictures, @Gene Howe

Will do Keith. Right now, all they are is a stack of ripped walnut. Start planing tomorrow.