hypocycloid - animated

7/27/2019 Hypocycloid - Animated

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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


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


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


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


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

hypocycloid - animated

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