mmx y Point #

15 0 0 114.99007 0.314978108 0.021014 2

14.960345 0.628568211 0.042028 314.91102 0.939397914 0.063042 414.84242 1.246125675 0.084056 5

14.754986 1.547455323 0.10507 6 Fomula of Lemniscate:14.649278 1.842149523 0.126084 7 x(t)=acos(t)/(1+(sint)^2)14.525959 2.129041915 0.147098 8 y(t)=asin(t)cos(t)/(1+(sint)^2)14.385786 2.407047681 0.168112 9

14.2296 2.675172367 0.189126 1014.058312 2.932518855 0.21014 11 Please input the parameters in yellow:

13.87289 3.178292422 0.231154 12 a13.674348 3.411803896 0.252168 13 15.00

13.46373 3.632470981 0.273182 1413.2421 3.839817845 0.294196 15 Note:

13.010528 4.033473133 0.31521 1612.77008 4.213166578 0.336224 17

12.521807 4.378724413 0.357238 1812.266737 4.530063782 0.378252 1912.005867 4.66718638 0.399266 2011.740154 4.790171518 0.42028 2111.470513 4.899168807 0.441294 22

11.19781 4.994390652 0.4623079 23 Preview:10.922857 5.076104708 0.4833219 2410.646415 5.144626442 0.5043359 2510.369189 5.200311919 0.5253499 2610.091826 5.243550907 0.5463639 279.8149196 5.274760374 0.5673779 289.5390064 5.294378432 0.5883919 299.2645703 5.302858774 0.6094059 308.9920429 5.3006656 0.6304199 318.7218058 5.288269073 0.6514339 328.4541934 5.266141266 0.6724479 338.1894949 5.234752617 0.6934619 347.9279573 5.194568846 0.7144759 357.6697882 5.146048325 0.7354899 367.4151585 5.089639863 0.7565039 377.1642051 5.025780873 0.7775179 386.9170336 4.954895897 0.7985319 396.6737212 4.877395434 0.8195459 406.4343188 4.79367507 0.8405599 416.1988538 4.704114843 0.8615739 42

5.967332 4.609078839 0.8825879 43

Angle t

1. t(min) means the start point of the curve, t(max) means the end point of the curve. Input N*Pi() in the cell according to your requirements (N is a variable).2. If you want to change the point numbers, please remain the same groups of data (x,y ), the default number is 300.

-20 -15 -10 -5 0 5 10 15 20

-6

-4

-2

0

2

4

6

Lemniscate

5.7397403 4.508914977 0.9036019 445.5160479 4.40395496 0.9246159 45

5.296209 4.294514367 0.9456299 465.0801638 4.180892866 0.9666439 474.8678407 4.063374527 0.9876579 484.6591573 3.942228211 1.0086719 494.4540219 3.817708035 1.0296859 504.2523348 3.690053879 1.0506999 51

4.053989 3.559491938 1.0717139 523.8588719 3.426235305 1.0927279 533.6668653 3.290484571 1.1137419 543.4778468 3.15242844 1.1347559 553.2916902 3.012244354 1.1557699 563.1082665 2.870099111 1.1767839 572.9274438 2.726149491 1.1977979 582.7490884 2.580542869 1.2188119 592.5730647 2.433417817 1.2398259 602.3992359 2.284904709 1.2608399 612.2274642 2.135126291 1.2818539 62

2.057611 1.984198261 1.3028679 631.8895373 1.832229821 1.3238819 641.7231034 1.679324217 1.3448959 651.5581698 1.525579267 1.3659098 661.3945966 1.37108788 1.3869238 671.2322438 1.215938548 1.4079378 681.0709717 1.060215845 1.4289518 690.9106405 0.904000897 1.4499658 700.7511105 0.747371851 1.4709798 710.5922422 0.590404335 1.4919938 720.4338962 0.433171906 1.5130078 730.2759331 0.275746495 1.5340218 740.1182135 0.118198843 1.5550358 75

-0.0394016 -0.039401064 1.5760498 76-0.1970515 -0.196983562 1.5970638 77-0.3548755 -0.354478879 1.6180778 78-0.5130127 -0.511816706 1.6390918 79-0.6716024 -0.668925761 1.6601058 80-0.8307841 -0.825733356 1.6811198 81-0.9906972 -0.982164953 1.7021338 82-1.1514814 -1.138143723 1.7231478 83-1.3132764 -1.293590085 1.7441618 84-1.4762219 -1.44842125 1.7651758 85-1.6404578 -1.602550744 1.7861898 86-1.8061241 -1.75588793 1.8072038 87-1.9733604 -1.908337507 1.8282178 88

-2.1423065 -2.059799007 1.8492318 89-2.3131015 -2.210166274 1.8702458 90-2.4858845 -2.359326927 1.8912598 91-2.6607936 -2.507161813 1.9122738 92-2.8379661 -2.653544445 1.9332878 93-3.0175384 -2.798340424 1.9543018 94

-3.199645 -2.941406851 1.9753158 95-3.3844188 -3.082591725 1.9963298 96-3.5719903 -3.221733334 2.0173438 97-3.7624873 -3.358659635 2.0383578 98-3.9560342 -3.493187636 2.0593718 99-4.1527511 -3.625122764 2.0803858 100-4.3527538 -3.754258254 2.1013998 101-4.5561522 -3.880374536 2.1224138 102-4.7630496 -4.003238644 2.1434278 103-4.9735419 -4.122603646 2.1644418 104-5.1877164 -4.238208114 2.1854558 105-5.4056502 -4.349775636 2.2064698 106-5.6274092 -4.457014388 2.2274838 107-5.8530464 -4.55961678 2.2484978 108-6.0826004 -4.657259188 2.2695117 109-6.3160932 -4.749601807 2.2905257 110

-6.553529 -4.836288617 2.3115397 111-6.7948912 -4.916947519 2.3325537 112-7.0401411 -4.991190637 2.3535677 113-7.2892149 -5.058614833 2.3745817 114-7.5420216 -5.118802462 2.3955957 115-7.7984402 -5.171322381 2.4166097 116-8.0583171 -5.215731273 2.4376237 117-8.3214635 -5.251575296 2.4586377 118-8.5876524 -5.2783921 2.4796517 119-8.8566161 -5.295713252 2.5006657 120

-9.128043 -5.303067081 2.5216797 121-9.4015756 -5.299981995 2.5426937 122-9.6768074 -5.285990276 2.5637077 123

-9.953281 -5.260632376 2.5847217 124-10.230486 -5.223461728 2.6057357 125-10.507858 -5.174050064 2.6267497 126-10.784777 -5.11199323 2.6477637 127-11.060566 -5.036917471 2.6687777 128-11.334492 -4.948486138 2.6897917 129

-11.60577 -4.846406751 2.7108057 130-11.873558 -4.730438341 2.7318197 131-12.136966 -4.600398955 2.7528337 132-12.395058 -4.456173202 2.7738477 133

-12.646856 -4.297719685 2.7948617 134-12.891347 -4.125078147 2.8158757 135

-13.12749 -3.938376148 2.8368897 136-13.354225 -3.737835066 2.8579037 137-13.570483 -3.523775206 2.8789177 138-13.775194 -3.296619822 2.8999317 139-13.967305 -3.056897825 2.9209457 140-14.145784 -2.805245002 2.9419597 141-14.309639 -2.542403578 2.9629737 142-14.457929 -2.269219988 2.9839877 143-14.589775 -1.986640769 3.0050017 144-14.704378 -1.695706546 3.0260157 145-14.801025 -1.397544125 3.0470297 146-14.879105 -1.093356775 3.0680437 147-14.938115 -0.784412856 3.0890577 148-14.977672 -0.472032982 3.1100717 149-14.997516 -0.157575988 3.1310857 150-14.997516 0.157575988 3.1520997 151-14.977672 0.472032982 3.1731137 152-14.938115 0.784412856 3.1941276 153-14.879105 1.093356775 3.2151416 154-14.801025 1.397544125 3.2361556 155-14.704378 1.695706546 3.2571696 156-14.589775 1.986640769 3.2781836 157-14.457929 2.269219988 3.2991976 158-14.309639 2.542403578 3.3202116 159-14.145784 2.805245002 3.3412256 160-13.967305 3.056897825 3.3622396 161-13.775194 3.296619822 3.3832536 162-13.570483 3.523775206 3.4042676 163-13.354225 3.737835066 3.4252816 164

-13.12749 3.938376148 3.4462956 165-12.891347 4.125078147 3.4673096 166-12.646856 4.297719685 3.4883236 167-12.395058 4.456173202 3.5093376 168-12.136966 4.600398955 3.5303516 169-11.873558 4.730438341 3.5513656 170

-11.60577 4.846406751 3.5723796 171-11.334492 4.948486138 3.5933936 172-11.060566 5.036917471 3.6144076 173-10.784777 5.11199323 3.6354216 174-10.507858 5.174050064 3.6564356 175-10.230486 5.223461728 3.6774496 176

-9.953281 5.260632376 3.6984636 177-9.6768074 5.285990276 3.7194776 178

-9.4015756 5.299981995 3.7404916 179-9.128043 5.303067081 3.7615056 180

-8.8566161 5.295713252 3.7825196 181-8.5876524 5.2783921 3.8035336 182-8.3214635 5.251575296 3.8245476 183-8.0583171 5.215731273 3.8455616 184-7.7984402 5.171322381 3.8665756 185-7.5420216 5.118802462 3.8875896 186-7.2892149 5.058614833 3.9086036 187-7.0401411 4.991190637 3.9296176 188-6.7948912 4.916947519 3.9506316 189

-6.553529 4.836288617 3.9716456 190-6.3160932 4.749601807 3.9926596 191-6.0826004 4.657259188 4.0136736 192-5.8530464 4.55961678 4.0346876 193-5.6274092 4.457014388 4.0557016 194-5.4056502 4.349775636 4.0767156 195-5.1877164 4.238208114 4.0977295 196-4.9735419 4.122603646 4.1187435 197-4.7630496 4.003238644 4.1397575 198-4.5561522 3.880374536 4.1607715 199-4.3527538 3.754258254 4.1817855 200-4.1527511 3.625122764 4.2027995 201-3.9560342 3.493187636 4.2238135 202-3.7624873 3.358659635 4.2448275 203-3.5719903 3.221733334 4.2658415 204-3.3844188 3.082591725 4.2868555 205

-3.199645 2.941406851 4.3078695 206-3.0175384 2.798340424 4.3288835 207-2.8379661 2.653544445 4.3498975 208-2.6607936 2.507161813 4.3709115 209-2.4858845 2.359326927 4.3919255 210-2.3131015 2.210166274 4.4129395 211-2.1423065 2.059799007 4.4339535 212-1.9733604 1.908337507 4.4549675 213-1.8061241 1.75588793 4.4759815 214-1.6404578 1.602550744 4.4969955 215-1.4762219 1.44842125 4.5180095 216-1.3132764 1.293590085 4.5390235 217-1.1514814 1.138143723 4.5600375 218-0.9906972 0.982164953 4.5810515 219-0.8307841 0.825733356 4.6020655 220-0.6716024 0.668925761 4.6230795 221-0.5130127 0.511816706 4.6440935 222-0.3548755 0.354478879 4.6651075 223

-0.1970515 0.196983562 4.6861215 224-0.0394016 0.039401064 4.7071355 2250.1182135 -0.118198843 4.7281495 2260.2759331 -0.275746495 4.7491635 2270.4338962 -0.433171906 4.7701775 2280.5922422 -0.590404335 4.7911915 2290.7511105 -0.747371851 4.8122055 2300.9106405 -0.904000897 4.8332195 2311.0709717 -1.060215845 4.8542335 2321.2322438 -1.215938548 4.8752475 2331.3945966 -1.37108788 4.8962615 2341.5581698 -1.525579267 4.9172755 2351.7231034 -1.679324217 4.9382895 2361.8895373 -1.832229821 4.9593035 237

2.057611 -1.984198261 4.9803175 2382.2274642 -2.135126291 5.0013314 2392.3992359 -2.284904709 5.0223454 2402.5730647 -2.433417817 5.0433594 2412.7490884 -2.580542869 5.0643734 2422.9274438 -2.726149491 5.0853874 2433.1082665 -2.870099111 5.1064014 2443.2916902 -3.012244354 5.1274154 2453.4778468 -3.15242844 5.1484294 2463.6668653 -3.290484571 5.1694434 2473.8588719 -3.426235305 5.1904574 248

4.053989 -3.559491938 5.2114714 2494.2523348 -3.690053879 5.2324854 2504.4540219 -3.817708035 5.2534994 2514.6591573 -3.942228211 5.2745134 2524.8678407 -4.063374527 5.2955274 2535.0801638 -4.180892866 5.3165414 254

5.296209 -4.294514367 5.3375554 2555.5160479 -4.40395496 5.3585694 2565.7397403 -4.508914977 5.3795834 257

5.967332 -4.609078839 5.4005974 2586.1988538 -4.704114843 5.4216114 2596.4343188 -4.79367507 5.4426254 2606.6737212 -4.877395434 5.4636394 2616.9170336 -4.954895897 5.4846534 2627.1642051 -5.025780873 5.5056674 2637.4151585 -5.089639863 5.5266814 2647.6697882 -5.146048325 5.5476954 2657.9279573 -5.194568846 5.5687094 2668.1894949 -5.234752617 5.5897234 2678.4541934 -5.266141266 5.6107374 268

8.7218058 -5.288269073 5.6317514 2698.9920429 -5.3006656 5.6527654 2709.2645703 -5.302858774 5.6737794 2719.5390064 -5.294378432 5.6947934 2729.8149196 -5.274760374 5.7158074 27310.091826 -5.243550907 5.7368214 27410.369189 -5.200311919 5.7578354 27510.646415 -5.144626442 5.7788494 27610.922857 -5.076104708 5.7998634 277

11.19781 -4.994390652 5.8208774 27811.470513 -4.899168807 5.8418914 27911.740154 -4.790171518 5.8629054 28012.005867 -4.66718638 5.8839194 28112.266737 -4.530063782 5.9049333 28212.521807 -4.378724413 5.9259473 283

12.77008 -4.213166578 5.9469613 28413.010528 -4.033473133 5.9679753 285

13.2421 -3.839817845 5.9889893 28613.46373 -3.632470981 6.0100033 287

13.674348 -3.411803896 6.0310173 28813.87289 -3.178292422 6.0520313 289

14.058312 -2.932518855 6.0730453 29014.2296 -2.675172367 6.0940593 291

14.385786 -2.407047681 6.1150733 29214.525959 -2.129041915 6.1360873 29314.649278 -1.842149523 6.1571013 29414.754986 -1.547455323 6.1781153 295

14.84242 -1.246125675 6.1991293 29614.91102 -0.939397914 6.2201433 297

14.960345 -0.628568211 6.2411573 29814.99007 -0.314978108 6.2621713 299

15 -3.67394E-15 6.2831853 300

Fomula of Lemniscate:x(t)=acos(t)/(1+(sint)^2)y(t)=asin(t)cos(t)/(1+(sint)^2)

Please input the parameters in yellow:t(min) t(max) Point number Delta

0.000000 6.283185 300 0.021014

t(min) means the start point of the curve, t(max) means the end point of the curve. Input N*Pi() in the cell according to your requirements (N is a variable).2. If you want to change the point numbers, please remain the same groups of data (x,y ), the default number is 300.

-20 -15 -10 -5 0 5 10 15 20

-6

-4

-2

0

2

4

6

Lemniscate