Triangles with no area (Posted on 2009-12-30)

	Submitted by brianjn
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Given values a, b and c as sides of a triangle none of those values may equal half of their sum. In Heron's formula for calculation of area that condition would produce a multiplier which is zero! My original spreadsheet read something like: a b c s A 1 2 3 3 0 Note this one 2 3 4 4.5 2.90473751 3 4 5 6 6 4 5 6 7.5 9.921567416 5 6 7 9 14.69693846 6 7 8 10.5 20.33316257 7 8 9 12 26.83281573 where in Heron's formula for triangular area we have: A= √s(s-a)(s-b)(s-c) The following listing generates data for all "triangles" having "zero" area with a maximum side of 50 units. CLS OPEN "notri.txt" FOR OUTPUT AS #1 FOR a = 1 TO 50 FOR b = 1 TO 50 FOR c = 1 TO 50 s = (a + b + c) / 2 m = (s * (s - a) * (s - b) * (s - c)) IF m = 0 THEN PRINT a; b; c; s; m PRINT #1, a; b; c; s; m END IF NEXT: NEXT: NEXT CLOSE 1

	Subject	Author	Date
	re(2): Removal?	brianjn	2010-01-01 20:04:08
	re: Removal?	Jer	2010-01-01 14:15:17
	Removal?	brianjn	2009-12-31 20:15:46
	re(3): most likely way - and apology	Charlie	2009-12-31 13:23:39
	re(2): most likely way - and apology	brianjn	2009-12-30 23:52:06
	re(3): most likely way	brianjn	2009-12-30 20:10:03
	re(2): most likely way	Charlie	2009-12-30 19:18:44
	re: most likely way	brianjn	2009-12-30 19:04:37
	most likely way	Charlie	2009-12-30 13:44:29