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MacOS 8.1

Win98

DOS

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|00000000| 47 53 50 63 0e 00 c8 00 | 71 01 00 00 00 00 b6 01 |GSPc....|q.......|
|00000010| 08 00 15 00 10 00 4c 02 | 00 00 46 69 76 65 20 50 |......L.|..Five P|
|00000020| 6f 69 6e 74 20 43 6f 6e | 69 63 0d 0a 43 6f 6e 73 |oint Con|ic..Cons|
|00000030| 74 72 75 63 74 73 20 74 | 68 65 20 6c 6f 63 75 73 |tructs t|he locus|
|00000040| 20 6f 66 20 74 68 65 20 | 75 6e 69 71 75 65 20 63 | of the |unique c|
|00000050| 6f 6e 69 63 20 73 65 63 | 74 69 6f 6e 20 70 61 73 |onic sec|tion pas|
|00000060| 73 69 6e 67 20 74 68 72 | 6f 75 67 68 20 74 68 65 |sing thr|ough the|
|00000070| 20 66 69 76 65 20 67 69 | 76 65 6e 20 70 6f 69 6e | five gi|ven poin|
|00000080| 74 73 2e 20 54 68 65 20 | 74 65 63 68 6e 69 71 75 |ts. The |techniqu|
|00000090| 65 20 75 73 65 73 20 50 | 61 73 63 61 6c 27 73 20 |e uses P|ascal's |
|000000a0| 74 68 65 6f 72 65 6d 20 | 77 68 69 63 68 20 73 74 |theorem |which st|
|000000b0| 61 74 65 73 20 74 68 61 | 74 20 66 6f 72 20 70 6f |ates tha|t for po|
|000000c0| 69 6e 74 73 20 41 2c 20 | 42 2c 20 43 2c 20 44 2c |ints A, |B, C, D,|
|000000d0| 20 45 2c 20 61 6e 64 20 | 46 20 6f 6e 20 61 20 63 | E, and |F on a c|
|000000e0| 6f 6e 69 63 2c 20 74 68 | 65 20 70 6f 69 6e 74 73 |onic, th|e points|
|000000f0| 20 64 65 74 65 72 6d 69 | 6e 65 64 20 62 79 20 74 | determi|ned by t|
|00000100| 68 65 20 69 6e 74 65 72 | 73 65 63 74 69 6f 6e 20 |he inter|section |
|00000110| 6f 66 20 41 42 20 61 6e | 64 20 44 45 2c 20 43 44 |of AB an|d DE, CD|
|00000120| 20 61 6e 64 20 41 46 2c | 20 61 6e 64 20 42 43 20 | and AF,| and BC |
|00000130| 61 6e 64 20 45 46 20 61 | 72 65 20 63 6f 6c 6c 69 |and EF a|re colli|
|00000140| 6e 65 61 72 2e 20 47 69 | 76 65 6e 20 66 69 76 65 |near. Gi|ven five|
|00000150| 20 70 6f 69 6e 74 73 2c | 20 74 68 69 73 20 63 6f | points,| this co|
|00000160| 6e 73 74 72 61 69 6e 74 | 20 64 65 74 65 72 6d 69 |nstraint| determi|
|00000170| 6e 65 73 20 74 68 65 20 | 6c 6f 63 75 73 20 6f 66 |nes the |locus of|
|00000180| 20 70 6f 73 73 69 62 6c | 65 20 73 69 78 74 68 20 | possibl|e sixth |
|00000190| 70 6f 69 6e 74 73 2e 0d | 0a 0d 0a 59 6f 75 20 63 |points..|...You c|
|000001a0| 61 6e 20 69 6e 63 72 65 | 61 73 65 20 74 68 65 20 |an incre|ase the |
|000001b0| 73 6d 6f 6f 74 68 6e 65 | 73 73 20 6f 66 20 74 68 |smoothne|ss of th|
|000001c0| 65 20 63 75 72 76 65 20 | 62 79 20 69 6e 63 72 65 |e curve |by incre|
|000001d0| 61 73 69 6e 67 20 74 68 | 65 20 6e 75 6d 62 65 72 |asing th|e number|
|000001e0| 20 6f 66 20 73 61 6d 70 | 6c 65 20 70 6f 69 6e 74 | of samp|le point|
|000001f0| 73 20 66 6f 72 20 74 68 | 65 20 6c 6f 63 75 73 2c |s for th|e locus,|
|00000200| 20 61 74 20 74 68 65 20 | 63 6f 73 74 20 6f 66 20 | at the |cost of |
|00000210| 73 6c 6f 77 69 6e 67 20 | 64 6f 77 6e 20 74 68 65 |slowing |down the|
|00000220| 20 72 65 73 70 6f 6e 73 | 69 76 65 6e 65 73 73 20 | respons|iveness |
|00000230| 6f 66 20 74 68 65 20 73 | 6b 65 74 63 68 2e 0d 42 |of the s|ketch..B|
|00000240| 69 6c 6c 20 46 69 6e 7a | 65 72 2c 33 2f 39 35 2e |ill Finz|er,3/95.|
|00000250| 20 28 54 68 61 6e 6b 73 | 20 74 6f 20 4a 69 6d 20 | (Thanks| to Jim |
|00000260| 4b 69 6e 67 2e 29 03 00 | 00 00 00 00 00 00 00 00 |King.)..|........|
|00000270| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000280| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000290| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002c0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000002f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000300| 00 00 13 00 00 00 2f 13 | 00 00 00 06 00 02 00 0d |....../.|........|
|00000310| 00 00 00 90 42 00 00 00 | 00 13 00 00 00 2f 13 00 |....B...|...../..|
|00000320| 00 00 06 00 03 00 0d 00 | 00 00 90 c2 00 00 00 80 |........|........|
|00000330| 0f 00 00 00 22 0f 00 00 | 00 04 00 04 00 0d 00 02 |...."...|........|
|00000340| 00 03 00 0b 00 00 00 21 | 0b 00 00 00 02 00 05 00 |.......!|........|
|00000350| 04 00 0d 00 00 00 01 0d | 00 00 00 03 00 06 00 0d |........|........|
|00000360| 00 05 00 0d 00 00 00 01 | 0d 00 00 00 03 00 07 00 |........|........|
|00000370| 0b 00 0d 00 0d 00 00 00 | 01 0d 00 00 00 03 00 0a |........|........|
|00000380| 00 08 00 01 00 0d 00 00 | 00 03 0d 00 00 00 03 00 |........|........|
|00000390| 0c 00 07 00 0a 00 0d 00 | 00 00 01 0d 00 00 00 03 |........|........|
|000003a0| 00 0e 00 08 00 09 00 0d | 00 00 00 03 0d 00 00 00 |........|........|
|000003b0| 03 00 0f 00 0e 00 06 00 | 0d 00 00 00 01 0d 00 00 |........|........|
|000003c0| 00 03 00 10 00 0f 00 0c | 00 0d 00 00 00 01 0d 00 |........|........|
|000003d0| 00 00 03 00 11 00 0b 00 | 09 00 0d 00 00 00 03 0d |........|........|
|000003e0| 00 00 00 03 00 12 00 11 | 00 10 00 0d 00 00 00 01 |........|........|
|000003f0| 0d 00 00 00 03 00 13 00 | 01 00 12 00 0d 00 00 00 |........|........|
|00000400| 03 0d 00 00 00 03 00 14 | 00 06 00 13 00 0f 00 00 |........|........|
|00000410| 00 37 0f 00 00 00 04 00 | 15 00 14 00 05 00 04 00 |.7......|........|
|00000420| 41 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |A.......|........|
|00000430| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000440| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000450| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000460| 00 00 00 00 00 00 00 00 | 00 00 00 03 00 ff 01 00 |........|........|
|00000470| 00 00 00 00 01 41 00 00 | 00 00 00 00 00 00 00 00 |.....A..|........|
|00000480| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000490| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000004c0| 03 00 02 00 00 01 00 00 | 00 00 42 00 00 00 00 00 |........|..B.....|
|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 00 00 00 00 00 00 |........|........|
|000004f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000500| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000510| 00 00 00 00 00 03 00 02 | 00 00 01 00 00 00 00 61 |........|.......a|
|00000520| 31 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |1.......|........|
|00000530| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000540| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|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 1a 00 02 00 00 01 |........|........|
|00000570| 00 00 00 00 43 00 00 00 | 00 00 00 00 00 00 00 00 |....C...|........|
|00000580| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000590| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000005b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 03 |........|........|
|000005c0| 00 02 00 00 01 00 00 00 | 00 6c 00 00 00 00 00 00 |........|.l......|
|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 00 00 00 00 00 00 00 |........|........|
|000005f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000600| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000610| 00 00 00 00 08 00 02 00 | 00 01 01 00 00 01 6a 00 |........|......j.|
|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 00 00 |........|........|
|00000640| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|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 08 00 02 00 00 01 00 |........|........|
|00000670| 00 00 00 42 00 00 00 00 | 00 00 00 00 00 00 00 00 |...B....|........|
|00000680| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000690| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|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 03 00 |........|........|
|000006c0| ff 01 00 00 00 00 00 01 | 43 00 00 00 00 00 00 00 |........|C.......|
|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 | 00 00 00 00 00 00 00 00 |........|........|
|000006f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000700| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000710| 00 00 00 03 00 ff 01 00 | 00 00 00 00 01 6b 00 00 |........|.....k..|
|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 00 00 00 |........|........|
|00000740| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|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 | 08 00 02 00 00 01 00 00 |........|........|
|00000770| 00 00 44 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |..D.....|........|
|00000780| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000790| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|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 03 00 ff |........|........|
|000007c0| 01 00 00 00 00 00 01 50 | 00 00 00 00 00 00 00 00 |.......P|........|
|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 00 | 00 00 00 00 00 00 00 00 |........|........|
|000007f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000800| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000810| 00 00 03 00 02 00 00 01 | 01 00 00 01 45 00 00 00 |........|....E...|
|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 00 00 00 00 |........|........|
|00000840| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|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 03 | 00 ff 01 00 00 00 00 00 |........|........|
|00000870| 01 6d 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |.m......|........|
|00000880| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000890| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008b0| 00 00 00 00 00 00 00 00 | 00 00 00 00 08 00 02 00 |........|........|
|000008c0| 00 01 01 00 00 01 51 00 | 00 00 00 00 00 00 00 00 |......Q.|........|
|000008d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000008f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000900| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000910| 00 03 00 02 00 00 01 01 | 00 00 01 6c 00 00 00 00 |........|...l....|
|00000920| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000930| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000940| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000950| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000960| 00 00 00 00 00 00 08 00 | 06 00 00 01 00 00 00 00 |........|........|
|00000970| 6d 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |m.......|........|
|00000980| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000990| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000009a0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000009b0| 00 00 00 00 00 00 00 00 | 00 00 00 08 00 02 00 00 |........|........|
|000009c0| 01 00 00 00 00 52 00 00 | 00 00 00 00 00 00 00 00 |.....R..|........|
|000009d0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000009e0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|000009f0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a00| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a10| 03 00 02 00 00 01 01 00 | 00 01 70 00 00 00 00 00 |........|..p.....|
|00000a20| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a30| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a40| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a50| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a60| 00 00 00 00 00 08 00 02 | 00 00 01 01 00 00 01 46 |........|.......F|
|00000a70| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a80| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000a90| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000aa0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000ab0| 00 00 00 00 00 00 00 00 | 00 00 03 00 02 00 00 01 |........|........|
|00000ac0| 01 00 00 01 46 00 00 00 | 00 00 00 00 00 00 00 00 |....F...|........|
|00000ad0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000ae0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000af0| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 00 |........|........|
|00000b00| 00 00 00 00 00 00 00 00 | 00 00 00 00 00 00 00 26 |........|.......&|
|00000b10| 00 02 00 00 00 00 00 00 | 00                      |........|.       |
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