hypocycloid - animated
TRANSCRIPT
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What is it?
The dazzling display is based on a hypocycloid curve, plotted on an XY (Scatter) chart. A hypocycloid is
a special plane curve that is generated by the trace of a fixed point on a small circle that rolls within a
larger circle. Hasbro's SpiroGraph is also based on this concept.
How do I control it?
Basically, just click the various controls to change various aspects of the image. The curve is determined
by three parameters: a, b, and t. You can adjust these manually by using the three scroller. Or, click
Random to generate random values for these three parameters. You can also control the line
smoothness (on or off), the presence of line markers, and the color (green or mulitcolored).
To turn animation on or off, click the Toggle Animation button. Control the speed of the animation by
using the scroller.
Favorites?
When you get a plot that you like, click the Add to Favorites button to store the three parameters. You
can then retrieve those parameters later. Use the Next and Previous buttons to scroll through all of thesaved favorites. These parameters are stored in column N:P. If a favorite is displayed, you'll see a number
in the upper left corner of the chart.
Who did this?
This workbook was created by John Walkenbach, of JWalk & Associates. Visit John's web site (The
Spreadsheet Page) at:
http://j-walk.com/ss
Can I share this with others?
Sure, this workbook can be freely distributed. But it may not be sold or distributed as part of any
commercial product without the written permission of JWalk & Associates.
http://j-walk.com/sshttp://j-walk.com/ss -
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Favorite 1 Options
Parameters
a: 243
b: 973
t: 963
Speed: 1
Smooth lines
Colors
Markers
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242.82 972.58 962.57
704.31 225.98 578.74
459.64 341.29 43.28
562.70 477.21 912.07
834.68 586.13 620.31
750.31 27.27 996.91
546.95 794.73 269.32
498.77 608.24 733.01
357.19 144.15 892.24
829.18 604.27 760.27
116.37 67.85 606.32
29.14 376.94 151.09
456.90 404.47 531.89
425.81 58.09 718.64
804.95 600.90 626.73
217.15 883.84 384.93
110.68 215.48 439.82
656.53 957.24 245.01
847.51 616.30 868.14
882.17 956.78 728.14
427.04 189.16 904.81
518.03 735.33 893.08
607.40 461.85 57.34
695.72 882.36 856.56
986.09 910.96 226.87
938.55 654.50 506.09
459.64 753.69 596.09
185.40 77.68 432.76
99.41 205.05 692.52
705.55 533.42 579.52
50.05 547.60 206.49575.87 431.60 732.52
824.58 718.79 895.97
771.60 358.10 412.00
650.00 535.00 382.00
185.40 77.68 432.76
986.09 910.96 226.87
979.83 401.37 283.00
979.83 401.37 296.00
432.00 770.00 389.00
186.01 583.36 83.00
628.75 542.07 156.30
938.55 654.50 518.00
22.00 781.00 653.00
601 377 67
101 200 710
101 404 710
498.77 608 751
1000 750 824
1000 750 718
297 594 329
297 594 289
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448 896 568
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a_inc b_inc t_inc Animate -1652.15 2867.927
242.82 972.58 962.57 0 186548.5 188443.3
a b t x y x(norm) y(norm)
1.00 1.00 1.00 1.00 0.00 0.00886177 -0.01521904
243.82 973.58 963.57 1,384.79 (863.73) 0.01627963 -0.01980255
486.65 1,946.17 1,926.15 2,950.41 (630.54) 0.02467219 -0.01856506
729.47 2,918.75 2,888.72 1,661.82 (165.15) 0.01776466 -0.01609546
972.29 3,891.34 3,851.30 (1,578.35) (2,850.65) 0.00039563 -0.03034641
1,215.11 4,863.92 4,813.87 (2,100.94) (7,838.78) -0.00240578 -0.05681657
1,457.94 5,836.51 5,776.45 782.77 (9,092.03) 0.01305249 -0.06346711
1,700.76 6,809.09 6,739.02 870.20 (3,970.02) 0.01352117 -0.03628648
1,943.58 7,781.68 7,701.60 (6,197.93) 1,267.86 -0.0243678 -0.00849098
2,186.40 8,754.26 8,664.17 (14,520.74) (495.12) -0.06898255 -0.01784647
2,429.23 9,726.84 9,626.75 (14,225.88) (5,718.10) -0.06740195 -0.04556291
2,672.05 10,699.43 10,589.32 (5,743.62) (3,355.53) -0.02193245 -0.03302559
2,914.87 11,672.01 11,551.90 (944.75) 9,154.13 0.00379206 0.03335857
3,157.69 12,644.60 12,514.47 (6,763.55) 19,741.63 -0.02739987 0.0895426
3,400.52 13,617.18 13,477.04 (13,575.29) 16,841.23 -0.06391442 0.07415122
3,643.34 14,589.77 14,439.62 (7,025.56) 6,295.51 -0.02880434 0.01818896
3,886.16 15,562.35 15,402.19 10,909.97 4,718.55 0.06733969 0.00982056
4,128.99 16,534.93 16,364.77 21,981.73 15,895.93 0.12669028 0.06913486
4,371.81 17,507.52 17,327.34 15,731.59 23,185.25 0.09318614 0.1078166
4,614.63 18,480.10 18,289.92 5,066.57 11,327.56 0.03601591 0.04489217
4,857.45 19,452.69 19,252.49 9,419.09 (10,861.81) 0.05934776 -0.0728587
5,100.28 20,425.27 20,215.07 26,537.45 (20,117.56) 0.15111135 -0.1219756
5,343.10 21,397.86 21,177.64 32,948.17 (10,192.22) 0.18547626 -0.06930543
5,585.92 22,370.44 22,140.22 15,480.79 (1,736.85) 0.09184175 -0.02443589
5,828.74 23,343.03 23,102.79 (8,705.56) (14,220.02) -0.03781008 -0.0906795
6,071.57 24,315.61 24,065.37 (13,599.78) (36,962.14) -0.06404568 -0.21136362
6,314.39 25,288.19 25,027.94 (159.48) (41,036.14) 0.00800153 -0.232982876,557.21 26,260.78 25,990.52 3,689.56 (18,576.64) 0.02863441 -0.1137985
6,800.03 27,233.36 26,953.09 (18,231.10) 4,486.26 -0.08887207 0.00858793
7,042.86 28,205.95 27,915.66 (45,301.06) 2,559.47 -0.23398153 -0.00163689
7,285.68 29,178.53 28,878.24 (45,636.99) (13,727.82) -0.23578232 -0.08806756
7,528.50 30,151.12 29,840.81 (19,707.94) (10,840.48) -0.09678873 -0.07274552
7,771.32 31,123.70 30,803.39 (1,402.88) 20,634.78 0.00133621 0.0942822
8,014.15 32,096.28 31,765.96 (12,171.45) 49,795.89 -0.0563891 0.24902958
8,256.97 33,068.87 32,728.54 (30,155.98) 45,210.59 -0.15279579 0.22469705
8,499.79 34,041.45 33,691.11 (18,981.49) 18,111.61 -0.09289453 0.08089269
8,742.62 35,014.04 34,653.69 20,812.71 8,271.37 0.12042366 0.0286741
8,985.44 35,986.62 35,616.26 49,047.16 29,129.89 0.27177546 0.13936265
9,228.26 36,959.21 36,578.84 38,726.24 47,253.75 0.21644979 0.235539379,471.08 37,931.79 37,541.41 13,305.77 27,075.08 0.08018249 0.12845853
9,713.91 38,904.38 38,503.99 15,225.17 (18,445.03) 0.09047147 -0.11310007
9,956.73 39,876.96 39,466.56 46,374.79 (42,226.33) 0.25745014 -0.23929878
10,199.55 40,849.54 40,429.13 62,789.38 (25,850.83) 0.34544112 -0.15239998
10,442.37 41,822.13 41,391.71 33,889.65 (5,202.02) 0.19052311 -0.04282428
10,685.20 42,794.71 42,354.28 (13,568.88) (21,290.73) -0.06388007 -0.12820119
10,928.02 43,767.30 43,316.86 (29,225.12) (61,707.43) -0.14780592 -0.34267787
11,170.84 44,739.88 44,279.43 (7,062.13) (74,427.43) -0.02900039 -0.41017827
11,413.66 45,712.47 45,242.01 5,824.48 (38,147.82) 0.04007875 -0.21765562
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11,656.49 46,685.05 46,204.58 (25,552.70) 6,587.89 -0.12811975 0.01974049
11,899.31 47,657.63 47,167.16 (72,934.14) 10,721.97 -0.38210968 0.04167853
12,142.13 48,630.22 48,129.73 (80,017.72) (16,330.84) -0.42008145 -0.10188084
12,384.96 49,602.80 49,092.31 (38,697.97) (18,920.34) -0.19858545 -0.11562237
12,627.78 50,575.39 50,054.88 (1,769.19) 27,286.84 -0.00062739 0.12958226
12,870.60 51,547.97 51,017.46 (11,844.88) 78,141.27 -0.05463849 0.39944817
13,113.42 52,520.56 51,980.03 (42,268.01) 77,883.27 -0.21772277 0.39807905
13,356.25 53,493.14 52,942.61 (32,801.61) 34,688.54 -0.16697783 0.16886037
13,599.07 54,465.73 53,905.18 26,070.33 10,535.88 0.14860733 0.04069105
13,841.89 55,438.31 54,867.75 75,950.20 36,397.65 0.41599018 0.17792998
14,084.71 56,410.89 55,830.33 67,073.23 68,115.69 0.36840488 0.34624607
14,327.54 57,383.48 56,792.90 25,722.84 45,863.58 0.14674461 0.22816224
14,570.36 58,356.06 57,755.48 18,630.72 (21,854.11) 0.10872707 -0.13119083
14,813.18 59,328.65 58,718.05 60,421.90 (65,721.57) 0.3327502 -0.36397942
15,056.00 60,301.23 59,680.63 90,926.17 (47,548.65) 0.49626943 -0.2675424
15,298.83 61,273.82 60,643.20 56,344.29 (11,972.74) 0.310892 -0.07875401
15,541.65 62,246.40 61,605.78 (14,986.95) (24,999.64) -0.07148166 -0.14788301
15,784.47 63,218.99 62,568.35 (47,683.14) (81,231.40) -0.24675075 -0.44628441
16,027.29 64,191.57 63,530.93 (20,275.49) (107,754.36) -0.09983111 -0.5870321116,270.12 65,164.15 64,493.50 5,766.84 (62,526.45) 0.03976975 -0.34702411
16,512.94 66,136.74 65,456.08 (28,759.75) 6,186.63 -0.14531124 0.01761116
16,755.76 67,109.32 66,418.65 (96,266.57) 22,963.52 -0.507184 0.10663996
16,998.59 68,081.91 67,381.22 (115,998.57) (12,791.76) -0.61295813 -0.08310024
17,241.41 69,054.49 68,343.80 (62,956.19) (26,094.99) -0.32862251 -0.15369562
17,484.23 70,027.08 69,306.37 (3,539.22) 29,325.53 -0.01011573 0.14040084
17,727.05 70,999.66 70,268.95 (6,475.59) 103,393.98 -0.02585621 0.53345505
17,969.88 71,972.24 71,231.52 (48,840.75) 113,728.11 -0.25295617 0.58829455
18,212.70 72,944.83 72,194.10 (47,097.94) 56,653.46 -0.24361379 0.28542022
18,455.52 73,917.41 73,156.67 26,500.38 13,014.04 0.15091267 0.05384172
18,698.34 74,890.00 74,119.25 101,172.62 38,004.96 0.55119589 0.18645939
18,941.17 75,862.58 75,081.82 99,959.84 84,438.64 0.54469474 0.43286619,183.99 76,835.17 76,044.40 43,288.05 66,514.08 0.24090357 0.33774691
19,426.81 77,807.75 77,006.97 21,040.28 (20,520.37) 0.12164359 -0.12411317
19,669.63 78,780.34 77,969.55 68,576.35 (89,056.08) 0.37646242 -0.48780717
19,912.46 79,752.92 78,932.12 115,856.40 (74,849.69) 0.62990881 -0.41241903
20,155.28 80,725.50 79,894.69 81,957.78 (23,296.88) 0.44819406 -0.1388471
20,398.10 81,698.09 80,857.27 (12,042.87) (26,556.39) -0.05569985 -0.1561441
20,640.93 82,670.67 81,819.84 (67,505.44) (95,029.49) -0.35300891 -0.51950584
20,883.75 83,643.26 82,782.42 (39,772.61) (139,449.41) -0.20434609 -0.75522617
21,126.57 84,615.84 83,744.99 2,076.33 (91,181.02) 0.01998663 -0.49908342
21,369.39 85,588.43 84,707.57 (28,782.58) 2,079.55 -0.14543363 -0.00418364
21,612.22 86,561.01 85,670.14 (114,425.72) 37,997.15 -0.60452676 0.18641797
21,855.04 87,533.59 86,632.72 (152,056.17) (2,724.60) -0.80624615 -0.0296775
22,097.86 88,506.18 87,595.29 (92,345.64) (30,830.76) -0.48616572 -0.17882664
22,340.68 89,478.76 88,557.87 (8,119.88) 27,336.31 -0.03467052 0.1298448
22,583.51 90,451.35 89,520.44 2,921.20 124,373.00 0.02451558 0.64478306
22,826.33 91,423.93 90,483.02 (49,100.19) 151,372.86 -0.25434693 0.78806148
23,069.15 92,396.52 91,445.59 (60,349.64) 84,276.05 -0.31465002 0.43200318
23,311.97 93,369.10 92,408.17 22,301.38 17,220.13 0.12840373 0.0761619
23,554.80 94,341.69 93,370.74 123,306.37 34,623.57 0.66984465 0.16851559
23,797.62 95,314.27 94,333.31 136,262.01 95,112.77 0.73929383 0.48950973
24,040.44 96,286.85 95,295.89 66,661.61 87,624.71 0.36619835 0.44977331
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24,283.27 97,259.44 96,258.46 23,971.10 (14,239.71) 0.13735433 -0.09078396
24,526.09 98,232.02 97,221.04 71,118.26 (110,692.19) 0.39008841 -0.60262212
24,768.91 99,204.61 98,183.61 136,210.43 (106,958.35) 0.73901732 -0.58280799
25,011.73 100,177.19 99,146.19 109,545.87 (40,181.84) 0.59608096 -0.22844941
25,254.56 101,149.78 100,108.76 (4,142.01) (27,375.97) -0.01334698 -0.16049334
25,497.38 102,122.36 101,071.34 (87,131.55) (102,969.09) -0.45821538 -0.56163843
25,740.20 103,094.94 102,033.91 (65,144.15) (167,977.81) -0.34035113 -0.90661599
25,983.02 104,067.53 102,996.49 (6,533.81) (123,229.13) -0.02616833 -0.66915108
26,225.85 105,040.11 103,959.06 (26,835.15) (6,679.46) -0.13499436 -0.05066448
26,468.67 106,012.70 104,921.64 (126,873.75) 54,348.47 -0.67125487 0.27318845
26,711.49 106,985.28 105,884.21 (186,597.45) 13,878.65 -0.99140592 0.05842989
26,954.31 107,957.87 106,846.78 (126,349.79) (31,649.37) -0.66844621 -0.18317072
27,197.14 108,930.45 107,809.36 (16,745.07) 22,246.59 -0.08090613 0.10283552
27,439.96 109,903.04 108,771.93 15,060.54 140,171.02 0.08958899 0.72861741
27,682.78 110,875.62 109,734.51 (42,618.96) 189,277.83 -0.21960406 0.98920934
27,925.60 111,848.20 110,697.08 (70,988.86) 117,444.61 -0.37168195 0.60801664
28,168.43 112,820.79 111,659.66 14,047.89 24,591.90 0.08416064 0.11528122
28,411.25 113,793.37 112,622.23 141,136.30 27,258.21 0.76542265 0.12943035
28,654.07 114,765.96 113,584.81 174,602.11 99,318.72 0.94481732 0.5118291828,896.90 115,738.54 114,547.38 96,147.77 107,647.13 0.52426002 0.556025
29,139.72 116,711.13 115,509.96 28,966.09 (3,191.59) 0.1641302 -0.03215564
29,382.54 117,683.71 116,472.53 68,700.50 (129,190.34) 0.37712791 -0.70078502
29,625.36 118,656.30 117,435.11 150,832.00 (142,757.13) 0.81739678 -0.77277906
29,868.19 119,628.88 118,397.68 137,688.44 (63,329.96) 0.74694025 -0.35128804
30,111.01 120,601.46 119,360.26 8,946.52 (28,999.80) 0.05681457 -0.1691104
30,353.83 121,574.05 120,322.83 (104,996.99) (105,303.68) -0.55398376 -0.57402722
30,596.65 122,546.63 121,285.40 (95,613.20) (191,925.59) -0.50368159 -1.03369812
30,839.48 123,519.22 122,247.98 (21,118.11) (157,479.72) -0.104348 -0.85090647
31,082.30 124,491.80 123,210.55 (24,349.93) (20,718.51) -0.12167225 -0.12516464
31,325.12 125,464.39 124,173.13 (133,444.74) 70,436.90 -0.70647891 0.35856386
31,567.94 126,436.97 125,135.70 (218,048.61) 36,638.85 -1.16000102 0.1792099631,810.77 127,409.55 126,098.28 (164,092.28) (27,215.10) -0.87076617 -0.15963963
32,053.59 128,382.14 127,060.85 (30,399.38) 15,279.17 -0.15410054 0.06586196
32,296.41 129,354.72 128,023.43 28,456.37 150,211.91 0.16139779 0.78190073
32,539.24 130,327.31 128,986.00 (29,348.85) 225,819.28 -0.14846914 1.18312148
32,782.06 131,299.89 129,948.58 (77,490.08) 155,661.96 -0.40653198 0.81082219
33,024.88 132,272.48 130,911.15 2,666.04 36,404.51 0.02314783 0.17796643
33,267.70 133,245.06 131,873.73 153,713.92 17,195.80 0.83284539 0.07603279
33,510.53 134,217.65 132,836.30 213,420.71 96,581.20 1.15290579 0.49730217
33,753.35 135,190.23 133,798.87 131,667.05 124,971.68 0.71466234 0.64796008
33,996.17 136,162.81 134,761.45 37,504.27 12,061.71 0.2098994 0.04878803
34,238.99 137,135.40 135,724.02 62,319.30 (143,293.76) 0.34292125 -0.77562676
34,481.82 138,107.98 136,686.60 158,849.12 (180,861.54) 0.86037281 -0.97498524
34,724.64 139,080.57 137,649.17 164,804.35 (93,088.95) 0.89229606 -0.50920815
34,967.46 140,053.15 138,611.75 27,066.71 (33,009.01) 0.1539485 -0.19038579
35,210.28 141,025.74 139,574.32 (119,622.90) (102,666.99) -0.63238643 -0.56003527
35,453.11 141,998.32 140,536.90 (130,069.44) (210,082.64) -0.68838552 -1.13005095
35,695.93 142,970.90 141,499.47 (42,431.09) (192,491.95) -0.21859696 -1.03670355
35,938.75 143,943.49 142,462.05 (22,900.40) (40,302.38) -0.11390201 -0.22908905
36,181.58 144,916.07 143,424.62 (134,362.98) 84,663.68 -0.71140119 0.43406021
36,424.40 145,888.66 144,387.20 (244,944.38) 64,800.50 -1.30417677 0.32865359
36,667.22 146,861.24 145,349.77 (204,375.70) (16,415.91) -1.08670687 -0.10233227
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36,910.04 147,833.83 146,312.34 (49,753.59) 7,889.55 -0.25784951 0.02664794
37,152.87 148,806.41 147,274.92 41,501.46 154,291.81 0.23132649 0.80355127
37,395.69 149,779.00 148,237.49 (9,634.19) 259,378.44 -0.04278801 1.3612077
37,638.51 150,751.58 149,200.07 (78,458.81) 198,061.22 -0.41172485 1.03581958
37,881.33 151,724.16 150,162.64 (10,609.86) 53,691.53 -0.0480181 0.26970231
38,124.16 152,696.75 151,125.22 160,418.38 5,939.10 0.86878493 0.01629757
38,366.98 153,669.33 152,087.79 251,058.94 86,805.66 1.35466689 0.44542693
38,609.80 154,641.92 153,050.37 172,747.75 138,017.20 0.93487691 0.71718787
38,852.62 155,614.50 154,012.94 50,912.89 30,595.86 0.2817768 0.14714203
39,095.45 156,587.09 154,975.52 53,266.52 (152,005.15) 0.29439353 -0.82185492
39,338.27 157,559.67 155,938.09 159,731.40 (219,689.88) 0.86510231 -1.18103307
39,581.09 158,532.25 156,900.67 189,235.83 (129,419.85) 1.02326188 -0.70200295
39,823.91 159,504.84 157,863.24 49,672.28 (40,934.17) 0.27512643 -0.23244173
40,066.74 160,477.42 158,825.82 (129,702.64) (96,047.42) -0.68641926 -0.52490765
40,309.56 161,450.01 159,788.39 (167,121.16) (221,516.69) -0.8870026 -1.19072726
40,552.38 162,422.59 160,750.96 (70,873.77) (226,648.18) -0.37106496 -1.21795821
40,795.21 163,395.18 161,713.54 (24,114.81) (65,305.06) -0.12041189 -0.36176917
41,038.03 164,367.76 162,676.11 (130,241.35) 95,502.41 -0.68930702 0.4915774
41,280.85 165,340.35 163,638.69 (266,013.32) 97,262.30 -1.41711756 0.5009164841,523.67 166,312.93 164,601.26 (245,737.81) 1,565.43 -1.30842995 -0.00691186
41,766.50 167,285.51 165,563.84 (75,115.28) 1,689.95 -0.39380173 -0.00625108
42,009.32 168,258.10 166,526.41 52,555.35 152,601.75 0.29058127 0.79458277
42,252.14 169,230.68 167,488.99 15,794.83 288,432.03 0.09352515 1.51538449
42,494.96 170,203.27 168,451.56 (72,715.17) 243,441.09 -0.38093586 1.27663398
42,737.79 171,175.85 169,414.14 (24,297.47) 77,176.95 -0.12139104 0.39433088
42,980.61 172,148.44 170,376.71 161,001.81 (4,872.05) 0.8719124 -0.04107321
43,223.43 173,121.02 171,339.29 285,847.72 70,295.97 1.54115338 0.35781602
43,466.25 174,093.60 172,301.86 218,537.80 145,321.15 1.18033616 0.75594729
43,709.08 175,066.19 173,264.43 70,285.81 51,164.47 0.38562603 0.25629213
43,951.90 176,038.77 174,227.01 43,065.68 (154,651.30) 0.23971155 -0.83589707
44,194.72 177,011.36 175,189.58 153,330.96 (257,544.62) 0.83079253 -1.3819143544,437.55 177,983.94 176,152.16 209,338.69 (171,884.29) 1.13102401 -0.92734627
44,680.37 178,956.53 177,114.73 75,843.42 (54,165.76) 0.41541781 -0.30265696
44,923.19 179,929.11 178,077.31 (134,181.43) (86,743.51) -0.710428 -0.47553517
45,166.01 180,901.70 179,039.88 (205,162.93) (225,634.50) -1.09092687 -1.21257897
45,408.84 181,874.28 180,002.46 (106,457.35) (258,237.72) -0.56181206 -1.38559239
45,651.66 182,846.86 180,965.03 (29,585.21) (95,202.15) -0.14973617 -0.52042212
45,894.48 183,819.45 181,927.61 (122,059.54) 101,587.73 -0.64544814 0.52386994
46,137.30 184,792.03 182,890.18 (280,254.95) 132,626.07 -1.49346034 0.68857912
46,380.13 185,764.62 183,852.76 (286,522.66) 27,193.94 -1.52705864 0.12908927
46,622.95 186,737.20 184,815.33 (106,397.04) (1,636.44) -0.56148875 -0.02390305
46,865.77 187,709.79 185,777.91 60,035.73 145,730.32 0.3306801 0.75811857
47,108.59 188,682.37 186,740.48 45,848.88 311,639.82 0.254631 1.63853977
47,351.42 189,654.96 187,703.05 (59,368.40) 290,319.22 -0.30939005 1.5253991
47,594.24 190,627.54 188,665.63 (36,740.77) 107,221.71 -0.18809379 0.55376743
47,837.06 191,600.12 189,628.20 155,616.21 (13,548.28) 0.84304269 -0.0871148
48,079.88 192,572.71 190,590.78 316,199.38 47,752.01 1.70385458 0.23818345
48,322.71 193,545.29 191,553.35 267,836.37 145,625.83 1.44460291 0.75756407
48,565.53 194,517.88 192,515.93 96,411.92 72,256.53 0.525676 0.36822001
48,808.35 195,490.46 193,478.50 33,394.55 (150,932.60) 0.18786911 -0.81616329
49,051.18 196,463.05 194,441.08 139,904.57 (292,701.58) 0.75881988 -1.56847953
49,294.00 197,435.63 195,403.65 223,574.00 (219,652.09) 1.20733286 -1.18083252
-
7/27/2019 Hypocycloid - Animated
26/29
49,536.82 198,408.21 196,366.23 104,323.30 (73,869.71) 0.56808519 -0.40721863
49,779.64 199,380.80 197,328.80 (132,324.74) (76,302.39) -0.70047511 -0.42012798
50,022.47 200,353.38 198,291.38 (242,455.82) (222,227.08) -1.29083672 -1.19449704
50,265.29 201,325.97 199,253.95 (148,786.03) (285,547.31) -0.78871644 -1.53051442
50,508.11 202,298.55 200,216.52 (40,776.20) (129,083.41) -0.20972585 -0.7002176
50,750.93 203,271.14 201,179.10 (111,122.96) 101,797.82 -0.58682224 0.52498483
50,993.76 204,243.72 202,141.67 (287,004.89) 169,262.22 -1.52964364 0.8829938
51,236.58 205,216.31 203,104.25 (324,963.43) 60,541.60 -1.73312173 0.30605314
51,479.40 206,188.89 204,066.82 (143,104.35) (427.02) -0.75825963 -0.01748508
51,722.22 207,161.47 205,029.40 62,509.14 134,645.96 0.34393891 0.69929792
51,965.05 208,134.06 205,991.97 79,125.29 327,925.00 0.43301037 1.72495926
52,207.87 209,106.64 206,954.55 (37,878.38) 337,001.28 -0.19419199 1.77312376
52,450.69 210,079.23 207,917.12 (46,195.19) 143,787.38 -0.23877456 0.74780813
52,693.52 211,051.81 208,879.70 144,820.68 (18,443.06) 0.78517289 -0.11308965
52,936.34 212,024.40 209,842.27 340,697.58 20,246.94 1.83517805 0.09222409
53,179.16 212,996.98 210,804.85 319,144.12 137,956.17 1.71963996 0.71686402
53,421.98 213,969.56 211,767.42 129,717.40 92,169.02 0.70421122 0.47388832
53,664.81 214,942.15 212,730.00 25,997.93 (140,954.62) 0.14821925 -0.76321379
53,907.63 215,914.73 213,692.57 120,115.70 (323,502.80) 0.65274094 -1.7319303654,150.45 216,887.32 214,655.14 230,596.69 (271,528.94) 1.24497824 -1.45612402
54,393.27 217,859.90 215,617.72 133,572.60 (100,912.22) 0.72487715 -0.55072335
54,636.10 218,832.49 216,580.29 (123,772.10) (66,444.01) -0.65462841 -0.36781314
54,878.92 219,805.07 217,542.87 (277,216.52) (211,496.51) -1.47717275 -1.13755381
55,121.74 220,777.66 218,505.44 (197,060.04) (306,954.20) -1.04749104 -1.64411296
55,364.56 221,750.24 219,468.02 (58,937.66) (165,685.48) -0.30708103 -0.89445143
55,607.39 222,722.82 220,430.59 (99,003.88) 95,326.72 -0.52185747 0.49064508
55,850.21 223,695.41 221,393.17 (285,984.56) 205,388.64 -1.5241741 1.07470351
56,093.03 224,667.99 222,355.74 (359,273.10) 101,265.51 -1.91703996 0.52216005
56,335.86 225,640.58 223,318.32 (184,343.80) 6,867.27 -0.97932517 0.02122305
56,578.68 226,613.16 224,280.89 58,776.55 120,659.48 0.32393021 0.62507677
56,821.50 227,585.75 225,243.47 113,970.94 336,543.29 0.61980171 1.7706933557,064.32 228,558.33 226,206.04 (8,100.98) 381,662.77 -0.03456917 2.01012602
57,307.15 229,530.91 227,168.61 (50,919.67) 186,419.35 -0.26410034 0.97404043
57,549.97 230,503.50 228,131.19 129,568.04 (18,045.37) 0.70341055 -0.11097926
57,792.79 231,476.08 229,093.76 358,180.85 (10,815.11) 1.92889776 -0.0726109
58,035.61 232,448.67 230,056.34 370,730.12 121,685.58 1.99616857 0.63052191
58,278.44 233,421.25 231,018.91 170,224.78 109,091.27 0.92135246 0.56368853
58,521.26 234,393.84 231,981.49 22,594.53 (125,239.97) 0.1299752 -0.67982186
58,764.08 235,366.42 232,944.06 95,016.02 (348,448.61) 0.51819321 -1.86430866
59,006.90 236,339.01 233,906.64 229,337.00 (326,003.48) 1.23822568 -1.74520051
59,249.73 237,311.59 234,869.21 161,840.21 (135,797.63) 0.87640666 -0.73584751
59,492.55 238,284.17 235,831.79 (108,573.53) (58,974.31) -0.57315592 -0.3281742
59,735.37 239,256.76 236,794.36 (307,711.31) (194,062.66) -1.64064114 -1.04503874
59,978.19 240,229.34 237,756.94 (250,099.39) (321,017.35) -1.33181038 -1.71874096
60,221.02 241,201.93 238,719.51 (85,025.90) (203,443.44) -0.44692799 -1.09481915
60,463.84 242,174.51 239,682.08 (87,467.30) 81,742.64 -0.46001521 0.41855934
60,706.66 243,147.10 240,644.66 (277,332.81) 239,159.63 -1.47779613 1.25391383
60,949.49 244,119.68 241,607.23 (387,738.98) 148,606.29 -2.06963233 0.77338031
61,192.31 245,092.27 242,569.81 (228,851.79) 21,591.88 -1.21791184 0.09936119
61,435.13 246,064.85 243,532.38 47,949.51 105,368.05 0.26589146 0.54393074
61,677.95 247,037.43 244,494.96 148,559.74 337,137.32 0.80521623 1.77384568
61,920.78 248,010.02 245,457.53 29,685.10 422,439.86 0.16798447 2.22651514
-
7/27/2019 Hypocycloid - Animated
27/29
62,163.60 248,982.60 246,420.11 (49,271.33) 234,250.42 -0.25526435 1.22786243
62,406.42 249,955.19 247,382.68 111,171.10 (11,068.25) 0.60479312 -0.07395422
62,649.24 250,927.77 248,345.26 367,815.90 (43,759.35) 1.9805468 -0.24743393
62,892.07 251,900.36 249,307.83 420,712.42 96,586.02 2.26410048 0.49732773
63,134.89 252,872.94 250,270.41 217,531.11 121,197.43 1.17493977 0.62793147
63,377.71 253,845.52 251,232.98 24,782.37 (104,719.45) 0.14170321 -0.57092695
63,620.53 254,818.11 252,195.56 66,006.76 (366,284.56) 0.36268803 -1.95895753
63,863.36 255,790.69 253,158.13 219,070.55 (381,311.70) 1.18319196 -2.03870109
64,106.18 256,763.28 254,120.70 187,246.60 (178,622.64) 1.01259854 -0.96310421
64,349.00 257,735.86 255,083.28 (87,206.26) (55,691.50) -0.45861589 -0.31075352
64,591.83 258,708.45 256,045.85 (332,350.30) (170,949.16) -1.77271935 -0.92238385
64,834.65 259,681.03 257,008.43 (306,387.29) (326,562.38) -1.63354371 -1.74816643
65,077.47 260,653.62 257,971.00 (119,637.02) (240,559.21) -0.63246214 -1.29177896
65,320.29 261,626.20 258,933.58 (78,384.87) 61,029.29 -0.4113285 0.30864114
65,563.12 262,598.78 259,896.15 (261,617.65) 268,760.81 -1.39355443 1.41099649
65,805.94 263,571.37 260,858.73 (408,816.36) 201,407.41 -2.18261842 1.0535766
66,048.76 264,543.95 261,821.30 (275,042.80) 44,806.00 -1.4655204 0.22255005
66,291.58 265,516.54 262,783.88 29,513.16 90,583.07 0.16706274 0.46547226
66,534.41 266,489.12 263,746.45 180,981.21 329,773.34 0.97901269 1.7347677466,777.23 267,461.71 264,709.03 74,771.91 457,525.08 0.40967392 2.41269957
67,020.05 268,434.29 265,671.60 (39,798.24) 286,025.28 -0.20448349 1.50261276
67,262.87 269,406.87 266,634.17 91,249.87 3,470.98 0.49800461 0.00320021
67,505.70 270,379.46 267,596.75 369,156.77 (76,716.02) 1.98773456 -0.42232296
67,748.52 271,352.04 268,559.32 467,148.81 62,859.97 2.51302441 0.31835588
67,991.34 272,324.63 269,521.90 270,806.81 126,742.65 1.46052606 0.65735794
68,234.16 273,297.21 270,484.47 33,947.15 (80,702.49) 0.19083132 -0.4434777
68,476.99 274,269.80 271,447.05 34,781.37 (376,078.87) 0.19530319 -2.01093237
68,719.81 275,242.38 272,409.62 199,473.37 (435,516.14) 1.07814059 -2.32634427
68,962.63 276,214.97 273,372.20 207,876.56 (229,049.33) 1.12318619 -1.23070022
69,205.46 277,187.55 274,334.77 (60,570.72) (58,289.54) -0.3158351 -0.32454034
69,448.28 278,160.13 275,297.35 (349,777.72) (143,548.73) -1.86613964 -0.7769797969,691.10 279,132.72 276,259.92 (364,131.93) (322,756.05) -1.94308591 -1.72796761
69,933.92 280,105.30 277,222.50 (162,956.04) (275,083.84) -0.86467532 -1.47498858
70,176.75 281,077.89 278,185.07 (73,640.55) 33,607.82 -0.38589643 0.16312541
70,419.57 282,050.47 279,147.65 (239,826.86) 292,505.58 -1.27674411 1.5370013
70,662.39 283,023.06 280,110.22 (421,217.07) 258,154.86 -2.24909287 1.35471459
70,905.21 283,995.64 281,072.79 (321,075.28) 77,211.34 -1.71227921 0.39451336
71,148.04 284,968.22 282,035.37 3,372.71 78,244.92 0.02693593 0.3999982
71,390.86 285,940.81 282,997.94 209,336.16 314,958.05 1.13101045 1.65614839
71,633.68 286,913.39 283,960.52 126,036.86 485,263.50 0.68448152 2.55989725
71,876.50 287,885.98 284,923.09 (21,325.93) 340,145.18 -0.10546199 1.78980731
72,119.33 288,858.56 285,885.67 71,661.57 26,182.99 0.39300085 0.12372455
72,362.15 289,831.15 286,848.24 362,186.77 (107,708.43) 1.95037161 -0.58678838
72,604.97 290,803.73 287,810.82 508,133.68 21,152.00 2.73272529 0.09702692
72,847.80 291,776.32 288,773.39 328,815.53 124,158.68 1.7714839 0.64364577
73,090.62 292,748.90 289,735.97 51,177.99 (54,827.71) 0.28319786 -0.30616971
73,333.44 293,721.48 290,698.54 3,251.74 (377,286.58) 0.02628745 -2.01734121
73,576.26 294,694.07 291,661.12 170,659.22 (486,596.32) 0.92368128 -2.59740812
73,819.09 295,666.65 292,623.69 221,876.84 (286,298.80) 1.19823519 -1.53450229
74,061.91 296,639.24 293,586.26 (29,965.37) (68,263.50) -0.15177402 -0.37746853
74,304.73 297,611.82 294,548.84 (358,953.61) (113,569.09) -1.91532734 -0.61788874
74,547.55 298,584.41 295,511.41 (421,343.90) (309,166.46) -2.24977272 -1.6558526
-
7/27/2019 Hypocycloid - Animated
28/29
74,790.38 299,556.99 296,473.99 (214,724.58) (305,010.25) -1.14218245 -1.63379712
75,033.20 300,529.58 297,436.56 (75,032.44) 337.90 -0.39335768 -0.01342592
75,276.02 301,502.16 298,399.14 (213,337.68) 308,928.61 -1.13474789 1.62415236
75,518.84 302,474.74 299,361.71 (423,988.41) 317,035.85 -2.26394875 1.66717452
75,761.67 303,447.33 300,324.29 (364,932.62) 119,096.01 -1.94737803 0.61678
76,004.49 304,419.91 301,286.86 (30,119.20) 70,328.31 -0.15259863 0.35798763
76,247.31 305,392.50 302,249.44 231,835.24 293,634.32 1.25161758 1.54299116
76,490.14 306,365.08 303,212.01 181,978.30 504,244.82 0.98435761 2.66062422
76,732.96 307,337.67 304,174.59 6,966.68 394,731.01 0.04620153 2.07947437
76,975.78 308,310.25 305,137.16 54,416.58 57,254.55 0.30055846 0.28860997
77,218.60 309,282.83 306,099.73 347,340.78 (134,749.28) 1.87078916 -0.7302843
77,461.43 310,255.42 307,062.31 541,896.56 (27,460.84) 2.91371241 -0.1609437
77,704.25 311,228.00 308,024.88 389,954.86 112,144.17 2.09922347 0.57988914
77,947.07 312,200.59 308,987.46 77,194.80 (28,995.57) 0.42266189 -0.16908795
78,189.89 313,173.17 309,950.03 (26,538.95) (369,796.90) -0.1334066 -1.97759623
78,432.72 314,145.76 310,912.61 133,196.61 (532,546.58) 0.72286161 -2.84124938
78,675.54 315,118.34 311,875.18 227,554.36 (349,166.27) 1.22866976 -1.86811702
78,918.36 316,090.93 312,837.76 2,958.93 (86,821.27) 0.02471786 -0.47594785
79,161.18 317,063.51 313,800.33 (359,223.06) (82,961.41) -1.91677175 -0.4554649579,404.01 318,036.09 314,762.91 (475,926.17) (285,805.84) -2.54236297 -1.53188633
79,646.83 319,008.68 315,725.48 (274,229.05) (328,372.17) -1.4611583 -1.75777028
79,889.65 319,981.26 316,688.06 (84,175.11) (37,502.71) -0.44236728 -0.21423225
80,132.47 320,953.85 317,650.63 (183,866.24) 316,871.97 -0.97676518 1.66630484
80,375.30 321,926.43 318,613.21 (416,578.68) 376,014.29 -2.22422858 1.98015159
80,618.12 322,899.02 319,575.78 (404,515.55) 170,296.55 -2.15956376 0.8884826
80,860.94 323,871.60 320,538.35 (70,156.00) 68,742.46 -0.36721738 0.34957213
81,103.77 324,844.18 321,500.93 246,895.67 267,155.49 1.33234956 1.40247767
81,346.59 325,816.77 322,463.50 240,770.84 513,386.93 1.29951717 2.70913802
81,589.41 326,789.35 323,426.08 45,485.72 447,702.52 0.25268427 2.36057486
81,832.23 327,761.94 324,388.65 41,583.64 96,415.52 0.23176701 0.49642293
82,075.06 328,734.52 325,351.23 325,506.37 (155,941.10) 1.75374503 -0.8427415782,317.88 329,707.11 326,313.80 566,897.71 (81,500.14) 3.04773197 -0.44771052
82,560.70 330,679.69 327,276.38 452,316.33 89,745.40 2.43351439 0.46102703
82,803.52 331,652.28 328,238.95 112,290.86 (5,285.61) 0.61079558 -0.04326784
83,046.35 332,624.86 329,201.53 (52,512.98) (353,961.30) -0.27264133 -1.8935625
83,289.17 333,597.44 330,164.10 88,104.49 (571,476.86) 0.4811437 -3.04783817
83,531.99 334,570.03 331,126.68 223,470.40 (416,057.38) 1.20677751 -2.22308374
83,774.81 335,542.61 332,089.25 36,263.46 (114,805.86) 0.20324796 -0.62445186
84,017.64 336,515.20 333,051.82 (350,369.28) (53,834.36) -1.86931073 -0.30089832
84,260.46 337,487.78 334,014.40 (525,772.66) (253,153.42) -2.80956687 -1.35861187
84,503.28 338,460.37 334,976.97 (340,310.48) (343,344.89) -1.81539019 -1.83722508
84,746.11 339,432.95 335,939.55 (102,407.23) (78,259.66) -0.54010124 -0.43051452
84,988.93 340,405.53 336,902.12 (153,398.70) 315,559.45 -0.81344284 1.6593398
85,231.75 341,378.12 337,864.70 (398,885.69) 432,919.92 -2.12938469 2.28212897
85,474.57 342,350.70 338,827.27 (437,742.26) 230,180.40 -2.33767671 1.20626435
85,717.40 343,323.29 339,789.85 (115,492.56) 75,230.66 -0.61024562 0.38400263
85,960.22 344,295.87 340,752.42 253,231.68 237,238.74 1.36631395 1.24372036
86,203.04 345,268.46 341,715.00 300,338.51 512,006.73 1.61883179 2.70181383
86,445.86 346,241.04 342,677.57 94,178.60 496,870.33 0.51370421 2.62149049
86,688.69 347,213.63 343,640.15 35,188.65 142,926.63 0.19748641 0.74324041
86,931.51 348,186.21 344,602.72 298,003.03 (169,576.18) 1.6063124 -0.91509795
87,174.33 349,158.79 345,565.30 581,916.29 (139,137.69) 3.12823965 -0.75357198
-
7/27/2019 Hypocycloid - Animated
29/29
87,417.15 350,131.38 346,527.87 513,762.57 56,423.37 2.76289915 0.28419922
87,659.98 351,103.96 347,490.44 156,293.85 14,138.07 0.84667522 0.05980655
87,902.80 352,076.55 348,453.02 (72,660.28) (330,600.27) -0.38064165 -1.76959405
88,145.62 353,049.13 349,415.59 36,826.04 (601,711.75) 0.20626371 -3.20828373
88,388.45 354,021.72 350,378.17 208,526.12 (485,044.75) 1.12666817 -2.58917451
88,631.27 354,994.30 351,340.74 67,802.55 (152,632.30) 0.37231442 -0.82518296
88,874.09 355,966.89 352,303.32 (332,647.60) (28,357.14) -1.77431303 -0.16570004
89,116.91 356,939.47 353,265.89 (568,871.03) (212,156.71) -3.04059722 -1.14105727
89,359.74 357,912.05 354,228.47 (411,396.19) (348,343.23) -2.19644767 -1.86374945
89,602.56 358,884.64 355,191.04 (130,708.83) (119,963.28) -0.69181296 -0.6518204
89,845.38 359,857.22 356,153.62 (124,106.70) 304,655.59 -0.65642201 1.60147698
90,088.20 360,829.81 357,116.19 (371,285.72) 485,547.31 -1.98143407 2.56140334
90,331.03 361,802.39 358,078.77 (462,651.50) 297,650.13 -2.4712036 1.56430158
90,573.85 362,774.98 359,041.34 (164,482.08) 91,273.76 -0.87285572 0.4691375
90,816.67 363,747.56 360,003.91 249,934.19 205,899.22 1.34863765 1.07741295
91,059.49 364,720.14 360,966.49 358,442.65 499,874.78 1.93030116 2.63743398
91,302.32 365,692.73 361,929.06 152,510.33 540,036.76 0.8263935 2.85055898