Given a plane X, a point M in the plane and a point N not in the plane.
Find all points R in X such that the ratio (NM + MR)/NR is the maximum.
(In reply to
re(2): solution (continued) by Charlie)
4.54000 3.41705 5.83095 4.54000 3.03506
4.55000 3.42203 5.83095 4.55000 3.03356
4.56000 3.42699 5.83095 4.56000 3.03209
4.57000 3.43191 5.83095 4.57000 3.03066
4.58000 3.43680 5.83095 4.58000 3.02926
4.59000 3.44166 5.83095 4.59000 3.02789
4.60000 3.44648 5.83095 4.60000 3.02655
4.61000 3.45128 5.83095 4.61000 3.02524
4.62000 3.45604 5.83095 4.62000 3.02397
4.63000 3.46076 5.83095 4.63000 3.02273
4.64000 3.46546 5.83095 4.64000 3.02152
4.65000 3.47011 5.83095 4.65000 3.02035
4.66000 3.47474 5.83095 4.66000 3.01921
4.67000 3.47933 5.83095 4.67000 3.01810
4.68000 3.48389 5.83095 4.68000 3.01702
4.69000 3.48841 5.83095 4.69000 3.01597
4.70000 3.49290 5.83095 4.70000 3.01496
4.71000 3.49735 5.83095 4.71000 3.01398
4.72000 3.50176 5.83095 4.72000 3.01304
4.73000 3.50615 5.83095 4.73000 3.01213
4.74000 3.51049 5.83095 4.74000 3.01125
4.75000 3.51480 5.83095 4.75000 3.01040
4.76000 3.51907 5.83095 4.76000 3.00958
4.77000 3.52331 5.83095 4.77000 3.00880
4.78000 3.52751 5.83095 4.78000 3.00806
4.79000 3.53168 5.83095 4.79000 3.00734
4.80000 3.53580 5.83095 4.80000 3.00666
4.81000 3.53989 5.83095 4.81000 3.00601
4.82000 3.54394 5.83095 4.82000 3.00540
4.83000 3.54796 5.83095 4.83000 3.00481
4.84000 3.55194 5.83095 4.84000 3.00426
4.85000 3.55588 5.83095 4.85000 3.00375
4.86000 3.55978 5.83095 4.86000 3.00326
4.87000 3.56364 5.83095 4.87000 3.00282
4.88000 3.56746 5.83095 4.88000 3.00240
4.89000 3.57125 5.83095 4.89000 3.00202
4.90000 3.57500 5.83095 4.90000 3.00167
4.91000 3.57871 5.83095 4.91000 3.00135
4.92000 3.58238 5.83095 4.92000 3.00107
4.93000 3.58601 5.83095 4.93000 3.00082
4.94000 3.58960 5.83095 4.94000 3.00060
4.95000 3.59315 5.83095 4.95000 3.00042
4.96000 3.59666 5.83095 4.96000 3.00027
4.97000 3.60014 5.83095 4.97000 3.00015
4.98000 3.60357 5.83095 4.98000 3.00007
4.99000 3.60696 5.83095 4.99000 3.00002
5.00000 3.61032 5.83095 5.00000 3.00000
5.01000 3.61363 5.83095 5.01000 3.00002
5.02000 3.61690 5.83095 5.02000 3.00007
5.03000 3.62014 5.83095 5.03000 3.00015
5.04000 3.62333 5.83095 5.04000 3.00027
5.05000 3.62648 5.83095 5.05000 3.00042
5.06000 3.62959 5.83095 5.06000 3.00060
5.07000 3.63266 5.83095 5.07000 3.00082
5.08000 3.63569 5.83095 5.08000 3.00107
5.09000 3.63868 5.83095 5.09000 3.00135
5.10000 3.64163 5.83095 5.10000 3.00167
5.11000 3.64453 5.83095 5.11000 3.00202
5.12000 3.64740 5.83095 5.12000 3.00240
5.13000 3.65023 5.83095 5.13000 3.00282
5.14000 3.65301 5.83095 5.14000 3.00326
5.15000 3.65575 5.83095 5.15000 3.00375
5.16000 3.65845 5.83095 5.16000 3.00426
5.17000 3.66111 5.83095 5.17000 3.00481
5.18000 3.66373 5.83095 5.18000 3.00540
5.19000 3.66631 5.83095 5.19000 3.00601
5.20000 3.66884 5.83095 5.20000 3.00666
5.21000 3.67133 5.83095 5.21000 3.00734
5.22000 3.67379 5.83095 5.22000 3.00806
5.23000 3.67620 5.83095 5.23000 3.00880
5.24000 3.67856 5.83095 5.24000 3.00958
5.25000 3.68089 5.83095 5.25000 3.01040
5.26000 3.68318 5.83095 5.26000 3.01125
5.27000 3.68542 5.83095 5.27000 3.01213
5.28000 3.68762 5.83095 5.28000 3.01304
5.29000 3.68978 5.83095 5.29000 3.01398
5.30000 3.69190 5.83095 5.30000 3.01496
5.31000 3.69398 5.83095 5.31000 3.01597
5.32000 3.69602 5.83095 5.32000 3.01702
5.33000 3.69801 5.83095 5.33000 3.01810
5.34000 3.69996 5.83095 5.34000 3.01921
5.35000 3.70188 5.83095 5.35000 3.02035
5.36000 3.70375 5.83095 5.36000 3.02152
5.37000 3.70557 5.83095 5.37000 3.02273
5.38000 3.70736 5.83095 5.38000 3.02397
5.39000 3.70911 5.83095 5.39000 3.02524
5.40000 3.71081 5.83095 5.40000 3.02655
5.41000 3.71247 5.83095 5.41000 3.02789
5.42000 3.71410 5.83095 5.42000 3.02926
5.43000 3.71568 5.83095 5.43000 3.03066
5.44000 3.71722 5.83095 5.44000 3.03209
5.45000 3.71871 5.83095 5.45000 3.03356
5.46000 3.72017 5.83095 5.46000 3.03506
5.47000 3.72159 5.83095 5.47000 3.03659
5.48000 3.72296 5.83095 5.48000 3.03816
5.49000 3.72430 5.83095 5.49000 3.03975
5.50000 3.72559 5.83095 5.50000 3.04138
5.51000 3.72685 5.83095 5.51000 3.04304
5.52000 3.72806 5.83095 5.52000 3.04473
5.53000 3.72923 5.83095 5.53000 3.04646
5.54000 3.73037 5.83095 5.54000 3.04821
5.55000 3.73146 5.83095 5.55000 3.05000
5.56000 3.73251 5.83095 5.56000 3.05182
5.57000 3.73352 5.83095 5.57000 3.05367
5.58000 3.73450 5.83095 5.58000 3.05555
5.59000 3.73543 5.83095 5.59000 3.05747
5.60000 3.73632 5.83095 5.60000 3.05941
5.61000 3.73718 5.83095 5.61000 3.06139
5.62000 3.73799 5.83095 5.62000 3.06340
5.63000 3.73877 5.83095 5.63000 3.06544
5.64000 3.73950 5.83095 5.64000 3.06751
5.65000 3.74020 5.83095 5.65000 3.06961
5.66000 3.74086 5.83095 5.66000 3.07174
5.67000 3.74148 5.83095 5.67000 3.07391
5.68000 3.74206 5.83095 5.68000 3.07610
5.69000 3.74260 5.83095 5.69000 3.07833
5.70000 3.74311 5.83095 5.70000 3.08058
5.71000 3.74357 5.83095 5.71000 3.08287
5.72000 3.74400 5.83095 5.72000 3.08519
5.73000 3.74439 5.83095 5.73000 3.08754
5.74000 3.74474 5.83095 5.74000 3.08992
5.75000 3.74506 5.83095 5.75000 3.09233
5.76000 3.74534 5.83095 5.76000 3.09477
5.77000 3.74558 5.83095 5.77000 3.09724
5.78000 3.74578 5.83095 5.78000 3.09974
5.79000 3.74595 5.83095 5.79000 3.10227
5.80000 3.74608 5.83095 5.80000 3.10483
5.81000 3.74617 5.83095 5.81000 3.10743
5.82000 3.74623 5.83095 5.82000 3.11005
5.83000 3.74625 5.83095 5.83000 3.11270
5.84000 3.74624 5.83095 5.84000 3.11538
5.85000 3.74619 5.83095 5.85000 3.11809
5.86000 3.74610 5.83095 5.86000 3.12083
5.87000 3.74598 5.83095 5.87000 3.12360
5.88000 3.74582 5.83095 5.88000 3.12640
5.89000 3.74563 5.83095 5.89000 3.12923
5.90000 3.74540 5.83095 5.90000 3.13209
5.91000 3.74514 5.83095 5.91000 3.13498
5.92000 3.74485 5.83095 5.92000 3.13790
5.93000 3.74452 5.83095 5.93000 3.14084
5.94000 3.74416 5.83095 5.94000 3.14382
5.95000 3.74376 5.83095 5.95000 3.14682
5.96000 3.74333 5.83095 5.96000 3.14986
5.97000 3.74287 5.83095 5.97000 3.15292
5.98000 3.74237 5.83095 5.98000 3.15601
5.99000 3.74184 5.83095 5.99000 3.15913
6.00000 3.74128 5.83095 6.00000 3.16228
6.01000 3.74068 5.83095 6.01000 3.16545
6.02000 3.74005 5.83095 6.02000 3.16866
6.03000 3.73939 5.83095 6.03000 3.17189
6.04000 3.73870 5.83095 6.04000 3.17515
6.05000 3.73798 5.83095 6.05000 3.17844
6.06000 3.73722 5.83095 6.06000 3.18176
6.07000 3.73644 5.83095 6.07000 3.18511
6.08000 3.73562 5.83095 6.08000 3.18848
6.09000 3.73477 5.83095 6.09000 3.19188
6.10000 3.73390 5.83095 6.10000 3.19531
6.11000 3.73299 5.83095 6.11000 3.19877
6.12000 3.73205 5.83095 6.12000 3.20225
6.13000 3.73108 5.83095 6.13000 3.20576
6.14000 3.73008 5.83095 6.14000 3.20930
6.15000 3.72906 5.83095 6.15000 3.21286
6.16000 3.72800 5.83095 6.16000 3.21646
6.17000 3.72691 5.83095 6.17000 3.22008
6.18000 3.72580 5.83095 6.18000 3.22372
6.19000 3.72466 5.83095 6.19000 3.22740
6.20000 3.72349 5.83095 6.20000 3.23110
6.21000 3.72229 5.83095 6.21000 3.23483
6.22000 3.72106 5.83095 6.22000 3.23858
6.23000 3.71981 5.83095 6.23000 3.24236
6.24000 3.71852 5.83095 6.24000 3.24617
6.25000 3.71722 5.83095 6.25000 3.25000
6.26000 3.71588 5.83095 6.26000 3.25386
6.27000 3.71452 5.83095 6.27000 3.25774
6.28000 3.71313 5.83095 6.28000 3.26166
6.29000 3.71172 5.83095 6.29000 3.26559
6.30000 3.71027 5.83095 6.30000 3.26956
6.31000 3.70881 5.83095 6.31000 3.27355
6.32000 3.70732 5.83095 6.32000 3.27756
6.33000 3.70580 5.83095 6.33000 3.28160
6.34000 3.70426 5.83095 6.34000 3.28567
6.35000 3.70269 5.83095 6.35000 3.28976
6.36000 3.70110 5.83095 6.36000 3.29387
6.37000 3.69948 5.83095 6.37000 3.29801
6.38000 3.69784 5.83095 6.38000 3.30218
6.39000 3.69618 5.83095 6.39000 3.30637
6.40000 3.69449 5.83095 6.40000 3.31059
6.41000 3.69278 5.83095 6.41000 3.31483
6.42000 3.69105 5.83095 6.42000 3.31910
6.43000 3.68929 5.83095 6.43000 3.32339
6.44000 3.68752 5.83095 6.44000 3.32770
6.45000 3.68571 5.83095 6.45000 3.33204
6.46000 3.68389 5.83095 6.46000 3.33641
6.47000 3.68205 5.83095 6.47000 3.34079
6.48000 3.68018 5.83095 6.48000 3.34521
6.49000 3.67829 5.83095 6.49000 3.34964
6.50000 3.67638 5.83095 6.50000 3.35410
6.51000 3.67445 5.83095 6.51000 3.35859
6.52000 3.67250 5.83095 6.52000 3.36309
6.53000 3.67052 5.83095 6.53000 3.36763
6.54000 3.66853 5.83095 6.54000 3.37218
6.55000 3.66652 5.83095 6.55000 3.37676
6.56000 3.66449 5.83095 6.56000 3.38136
6.57000 3.66243 5.83095 6.57000 3.38599
6.58000 3.66036 5.83095 6.58000 3.39063
6.59000 3.65827 5.83095 6.59000 3.39531
6.60000 3.65616 5.83095 6.60000 3.40000
6.61000 3.65403 5.83095 6.61000 3.40472
6.62000 3.65189 5.83095 6.62000 3.40946
6.63000 3.64972 5.83095 6.63000 3.41422
6.64000 3.64754 5.83095 6.64000 3.41901
6.65000 3.64534 5.83095 6.65000 3.42381
6.66000 3.64312 5.83095 6.66000 3.42864
6.67000 3.64088 5.83095 6.67000 3.43350
6.68000 3.63863 5.83095 6.68000 3.43837
6.69000 3.63636 5.83095 6.69000 3.44327
6.70000 3.63407 5.83095 6.70000 3.44819
6.71000 3.63176 5.83095 6.71000 3.45313
6.72000 3.62944 5.83095 6.72000 3.45809
6.73000 3.62711 5.83095 6.73000 3.46308
6.74000 3.62476 5.83095 6.74000 3.46808
6.75000 3.62239 5.83095 6.75000 3.47311
6.76000 3.62000 5.83095 6.76000 3.47816
6.77000 3.61760 5.83095 6.77000 3.48323
6.78000 3.61519 5.83095 6.78000 3.48832
6.79000 3.61276 5.83095 6.79000 3.49344
6.80000 3.61032 5.83095 6.80000 3.49857
6.81000 3.60786 5.83095 6.81000 3.50373
6.82000 3.60539 5.83095 6.82000 3.50890
6.83000 3.60290 5.83095 6.83000 3.51410
6.84000 3.60040 5.83095 6.84000 3.51932
6.85000 3.59789 5.83095 6.85000 3.52456
6.86000 3.59536 5.83095 6.86000 3.52982
6.87000 3.59282 5.83095 6.87000 3.53510
6.88000 3.59026 5.83095 6.88000 3.54040
6.89000 3.58770 5.83095 6.89000 3.54572
6.90000 3.58512 5.83095 6.90000 3.55106
6.91000 3.58253 5.83095 6.91000 3.55642
6.92000 3.57992 5.83095 6.92000 3.56180
6.93000 3.57730 5.83095 6.93000 3.56720
6.94000 3.57468 5.83095 6.94000 3.57262
6.95000 3.57204 5.83095 6.95000 3.57806
6.96000 3.56938 5.83095 6.96000 3.58352
6.97000 3.56672 5.83095 6.97000 3.58900
6.98000 3.56405 5.83095 6.98000 3.59450
6.99000 3.56136 5.83095 6.99000 3.60001
7.00000 3.55867 5.83095 7.00000 3.60555
DEFDBL A-Z
ptNx = 5: ptNy = 3
MN = SQR(ptNx * ptNx + ptNy * ptNy)
OPEN "find points max ratio.txt" FOR OUTPUT AS #2
'FOR ptRx = 5.8 TO 5.878 STEP .001
' DO
bg = -7: fin = 7: stp = .01
FOR ptRx = bg TO fin STEP stp
MR = ptRx
NR = SQR((ptRx - ptNx) * (ptRx - ptNx) + ptNy * ptNy)
v = (MN + MR) / NR
PRINT #2, USING " ##.#####"; ptRx; v;
PRINT #2, " ";
PRINT #2, USING " #####.#####"; MN; MR; NR
NEXT
' LOOP
CLOSE #2
|
|
Posted by Charlie
on 2015-06-05 16:02:17 |
re(3): solution (continued)
