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|00000000| 47 53 50 63 0e 00 c8 00 | 42 01 00 00 00 00 56 01 |GSPc....|B.....V.|
|00000010| 06 00 0d 00 0b 00 38 03 | 00 00 43 65 6e 74 72 6f |......8.|..Centro|
|00000020| 69 64 0d 0a 54 68 69 73 | 20 73 63 72 69 70 74 20 |id..This| script |
|00000030| 63 6f 6e 73 74 72 75 63 | 74 73 20 74 68 65 20 63 |construc|ts the c|
|00000040| 65 6e 74 72 6f 69 64 20 | 6f 66 20 61 20 74 72 69 |entroid |of a tri|
|00000050| 61 6e 67 6c 65 20 67 69 | 76 65 6e 20 74 68 65 20 |angle gi|ven the |
|00000060| 74 68 72 65 65 20 76 65 | 72 74 69 63 65 73 20 6f |three ve|rtices o|
|00000070| 66 20 74 68 65 20 74 72 | 69 61 6e 67 6c 65 2e 0d |f the tr|iangle..|
|00000080| 0a 0d 0a 54 68 65 20 63 | 65 6e 74 72 6f 69 64 20 |...The c|entroid |
|00000090| 69 73 20 61 6c 73 6f 20 | 63 61 6c 6c 65 64 20 74 |is also |called t|
|000000a0| 68 65 20 22 63 65 6e 74 | 65 72 20 6f 66 20 67 72 |he "cent|er of gr|
|000000b0| 61 76 69 74 79 2e 22 20 | 20 49 66 20 79 6f 75 20 |avity." | If you |
|000000c0| 77 65 72 65 20 74 6f 20 | 63 75 74 20 74 68 65 20 |were to |cut the |
|000000d0| 74 72 69 61 6e 67 6c 65 | 20 6f 75 74 20 6f 66 20 |triangle| out of |
|000000e0| 68 65 61 76 79 20 63 61 | 72 64 62 6f 61 72 64 20 |heavy ca|rdboard |
|000000f0| 61 6e 64 20 62 61 6c 61 | 6e 63 65 20 69 74 20 6f |and bala|nce it o|
|00000100| 6e 20 61 20 66 69 6e 67 | 65 72 74 69 70 2c 20 79 |n a fing|ertip, y|
|00000110| 6f 75 72 20 66 69 6e 67 | 65 72 20 77 6f 75 6c 64 |our fing|er would|
|00000120| 20 62 65 20 61 74 20 6f | 72 20 6e 65 61 72 20 74 | be at o|r near t|
|00000130| 68 65 20 74 72 69 61 6e | 67 6c 65 27 73 20 63 65 |he trian|gle's ce|
|00000140| 6e 74 72 6f 69 64 2e 0d | 0a 0d 0a 2a 20 20 43 6f |ntroid..|...*  Co|
|00000150| 6e 73 74 72 75 63 74 20 | 74 68 65 20 70 6f 6c 79 |nstruct |the poly|
|00000160| 67 6f 6e 20 69 6e 74 65 | 72 69 6f 72 73 20 6f 66 |gon inte|riors of|
|00000170| 20 74 68 65 20 73 69 78 | 20 73 6d 61 6c 6c 20 74 | the six| small t|
|00000180| 72 69 61 6e 67 6c 65 73 | 20 66 6f 72 6d 65 64 20 |riangles| formed |
|00000190| 62 79 20 74 68 65 20 6d | 65 64 69 61 6e 73 2e 20 |by the m|edians. |
|000001a0| 20 28 45 61 63 68 20 6f | 66 20 74 68 65 73 65 20 | (Each o|f these |
|000001b0| 73 6d 61 6c 6c 20 74 72 | 69 61 6e 67 6c 65 73 20 |small tr|iangles |
|000001c0| 68 61 73 20 61 20 74 72 | 69 61 6e 67 6c 65 20 76 |has a tr|iangle v|
|000001d0| 65 72 74 65 78 2c 20 61 | 20 6d 69 64 70 6f 69 6e |ertex, a| midpoin|
|000001e0| 74 2c 20 61 6e 64 20 74 | 68 65 20 63 65 6e 74 72 |t, and t|he centr|
|000001f0| 6f 69 64 20 61 73 20 76 | 65 72 74 69 63 65 73 2e |oid as v|ertices.|
|00000200| 29 20 20 57 68 61 74 20 | 73 65 65 6d 73 20 74 6f |)  What |seems to|
|00000210| 20 62 65 20 74 68 65 20 | 72 65 6c 61 74 69 6f 6e | be the |relation|
|00000220| 73 68 69 70 20 61 6d 6f | 6e 67 20 74 68 65 73 65 |ship amo|ng these|
|00000230| 20 74 72 69 61 6e 67 6c | 65 73 27 20 61 72 65 61 | triangl|es' area|
|00000240| 73 3f 0d 0a 0d 0a 2a 20 | 20 43 6f 6e 73 74 72 75 |s?....* | Constru|
|00000250| 63 74 20 74 68 65 20 69 | 6e 74 65 72 73 65 63 74 |ct the i|ntersect|
|00000260| 69 6f 6e 20 6f 66 20 74 | 77 6f 20 6f 66 20 74 68 |ion of t|wo of th|
|00000270| 65 20 74 72 69 61 6e 67 | 6c 65 27 73 20 61 6e 67 |e triang|le's ang|
|00000280| 6c 65 20 62 69 73 65 63 | 74 6f 72 73 2e 20 20 54 |le bisec|tors.  T|
|00000290| 68 69 73 20 70 6f 69 6e | 74 20 69 73 20 74 68 65 |his poin|t is the|
|000002a0| 20 74 72 61 6e 67 6c 65 | 27 73 20 22 69 6e 63 65 | trangle|'s "ince|
|000002b0| 6e 74 65 72 2e 22 20 20 | 44 72 61 67 20 74 68 65 |nter."  |Drag the|
|000002c0| 20 74 72 69 61 6e 67 6c | 65 20 75 6e 74 69 6c 20 | triangl|e until |
|000002d0| 74 68 65 20 69 6e 63 65 | 6e 74 65 72 20 61 6e 64 |the ince|nter and|
|000002e0| 20 74 68 65 20 63 65 6e | 74 72 6f 69 64 20 6f 76 | the cen|troid ov|
|000002f0| 65 72 6c 61 70 2e 20 20 | 57 68 61 74 20 6d 75 73 |erlap.  |What mus|
|00000300| 74 20 62 65 20 74 72 75 | 65 20 61 62 6f 75 74 20 |t be tru|e about |
|00000310| 74 68 65 20 74 72 69 61 | 6e 67 6c 65 20 66 6f 72 |the tria|ngle for|
|00000320| 20 74 68 65 73 65 20 74 | 77 6f 20 70 6f 69 6e 74 | these t|wo point|
|00000330| 73 20 74 6f 20 62 65 20 | 74 68 65 20 73 61 6d 65 |s to be |the same|
|00000340| 3f 0d 4e 2e 20 4a 61 63 | 6b 69 77 20 2a 20 33 2f |?.N. Jac|kiw * 3/|
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|000003c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000003d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000003e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 0d 00 |........|........|
|000003f0| 00 00 01 0d 00 00 00 03 | 00 03 00 02 00 01 00 0d |........|........|
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|00000420| 00 0b 00 00 00 00 0b 00 | 00 00 02 00 07 00 06 00 |........|........|
|00000430| 0b 00 00 00 00 0b 00 00 | 00 02 00 08 00 05 00 0b |........|........|
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|00000470| 0d 00 00 00 01 0d 00 00 | 00 03 00 0c 00 09 00 04 |........|........|
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|00000490| 0a 00 09 00 00 00 05 09 | 00 00 00 01 00 0d 00 56 |........|.......V|
|000004a0| 65 72 74 65 78 31 00 00 | 00 00 00 00 00 00 00 00 |ertex1..|........|
|000004b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004e0| 00 00 00 00 00 00 00 00 | 00 00 03 00 00 01 01 01 |........|........|
|000004f0| 01 00 00 01 56 65 72 74 | 65 78 32 00 00 00 00 00 |....Vert|ex2.....|
|00000500| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000510| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000520| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000530| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 03 |........|........|
|00000540| 00 00 01 00 00 00 00 00 | 01 6a 00 00 00 00 00 00 |........|.j......|
|00000550| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000560| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000570| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000580| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000590| 00 00 00 00 0a 00 02 00 | 00 00 00 00 00 00 56 65 |........|......Ve|
|000005a0| 72 74 65 78 33 00 00 00 | 00 00 00 00 00 00 00 00 |rtex3...|........|
|000005b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005e0| 00 00 00 00 00 00 00 00 | 00 03 00 00 01 00 00 00 |........|........|
|000005f0| 00 00 01 6b 00 00 00 00 | 00 00 00 00 00 00 00 00 |...k....|........|
|00000600| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000610| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000620| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000630| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 0a 00 |........|........|
|00000640| 02 00 00 00 00 00 00 00 | 6d 00 00 00 00 00 00 00 |........|m.......|
|00000650| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000660| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000670| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000680| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000690| 00 00 00 0a 00 02 00 00 | 00 00 00 00 00 44 00 00 |........|.....D..|
|000006a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000006b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000006c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000006d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000006e0| 00 00 00 00 00 00 00 00 | 07 00 00 00 01 00 01 00 |........|........|
|000006f0| 00 00 45 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |..E.....|........|
|00000700| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000710| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000720| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000730| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 07 00 00 |........|........|
|00000740| 00 01 00 01 00 00 00 46 | 00 00 00 00 00 00 00 00 |.......F|........|
|00000750| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000760| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000770| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000780| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000790| 00 00 07 00 00 00 01 00 | 01 00 00 00 6e 00 00 00 |........|....n...|
|000007a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007e0| 00 00 00 00 00 00 00 0a | 00 02 00 00 00 00 00 00 |........|........|
|000007f0| 00 70 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.p......|........|
|00000800| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000810| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000820| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000830| 00 00 00 00 00 00 00 00 | 00 00 00 00 0a 00 02 00 |........|........|
|00000840| 00 00 00 00 00 00 71 00 | 00 00 00 00 00 00 00 00 |......q.|........|
|00000850| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000860| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000870| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000880| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000890| 00 0a 00 02 00 00 00 00 | 00 00 00 43 65 6e 74 72 |........|...Centr|
|000008a0| 6f 69 64 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |oid.....|........|
|000008b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008e0| 00 00 00 00 00 00 03 00 | 00 00 01 00 01 00 00 01 |........|........|
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