[Icehouse] Re: Isosceles triangle angle

[David Artman]

> (*cought*1.75, a.k.a. 7/4*cough*)

Yeah, right. Same ratio.

BUT... I haven't seen anyone else derive the Base from the
 previous piece's Base. That's where I think all these other
 formulas go wrong: they are looking for a consistent formula
 for any given pip count X, but I do not think that is how
 they were originally invented. But by going *just* on what's
 been published about dimensions for 1, 2, and 3 pips, and
 suspecting that the 1 Height = 3 Base is the *only* intentional
 relationship; I think Base(x) = Base(x-1) + 0.21875 is the best
 way to figure any other sizes.

>From a spreadsheet:
Pips	Base	Height
-2     -0.0938 -0.1641 * Hence, nothing below neg1 is possible
-1	0.1250	0.2188 * Less than 1/4" x 1/8": bring tweezers!
0	0.3438	0.6016
1	0.5625	1.0000
2	0.7813	1.3750
3	1.0000	1.7500
4	1.2188	2.1328
5	1.4375	2.5156
6	1.6563	2.8984
7	1.8750	3.2813
8	2.0938	3.6641
9	2.3125	4.0469
10	2.5313	4.4297
11	2.7500	4.8125
12	2.9688	5.1953
13	3.1875	5.5781
14	3.4063	5.9609
15	3.6250	6.3438
16	3.8438	6.7266
17	4.0625	7.1094
18	4.2813	7.4922
19	4.5000	7.8750
20	4.7188	8.2578
21	4.9375	8.6406
22	5.1563	9.0234
23	5.3750	9.4063
24	5.5938	9.7891
25	5.8125	10.1719
26	6.0313	10.5547
27	6.2500	10.9375
28	6.4688	11.3203
29	6.6875	11.7031
30	6.9063	12.0859

It's interesting how few of the extended dimensions actually
 hit on "round" numbers--a TON of them have to be resolved to
 64ths or higher denominator fractions....

Are we done, yet? ;)
David