Wednesday, July 3, 2013

Using Monte Carlo Simulation to Determine Value of Pi in Excel

Monte Carlo methods use random values to generate something that is not random. So today, I will use Excel to generate random numbers and then calculate the value of Pi, which is approx. 3.14. Pi is used to measure the area of a circle. Basically what our plan is to generate a circle with radius 1.0 from the origin and from the equation of a circle (Area = Pi*r*r) we can see that the area of a circle with radius 1 is Pi. We will use excel to generate random values for X-Coordinate and Y-Coordinate and then graph them. What you will see after you graph the (x,y) is a rectangle, with length 2 and width 2. Next we will separate the values for (x,y) that hit inside the circle with radius 1 from the ones that hit outside of the circle. We can do that by using the formula X^2 + Y^2 = R^2. Afterward, we will calculate the area of the circle and area of the rectangle. From their we will calculate the value of Pi.

To get started with open up Excel. The Excel command for generating random numbers is RAND(). You can test by the Random command by typing =Rand() in any cell and you will get a Rand number between 0 and 1. To generate a circle with radius 1, you need to get random numbers between 1 and -1. The command you will type is get that is =1-(2*RAND()) in two columns for X and Y and you can drag that down to as many random numbers you want. To get a value close to Pi you will need to generate over 1000 points for (x,y). The more points you use the more accurate the value of Pi. So I will use 1000 points and you can see my values below:




NUMS X
Y
1 -0.3753
0.393222
2 -0.52305
-0.63836
3 0.645948
-0.09952
4 -0.45835
0.530955
5 -0.65366
-0.61368
6 0.840407
-0.6665
7 -0.18093
0.182653
8 0.382593
0.837658
9 0.765181
0.854358
10 0.784243
-0.96181
11 0.753266
0.227069
12 -0.87169
-0.1506
13 -0.4961
0.034662
14 -0.13412
-0.96387
15 -0.24221
0.345125
16 -0.24996
-0.72305
17 0.417938
-0.20437
18 -0.51827
-0.94565
19 0.412481
-0.67224
20 0.831408
0.778381
21 0.189574
0.234717
22 -0.91913
0.813221
23 -0.92543
0.622006
24 0.7278
-0.21911
25 -0.96766
-0.64161
26 -0.71109
0.565655
27 0.955577
0.745066
28 -0.68654
-0.30849
29 0.339207
0.86824
30 0.456058
-0.58421
31 0.809588
0.198191
32 0.405219
-0.08023
33 -0.9394
-0.79732
34 0.175434
0.902226
35 -0.61469
-0.24193
36 0.33836
-0.48176
37 -0.5494
-0.39721
38 0.176253
0.816443
39 -0.32524
-0.23104
40 -0.93887
-0.49109
41 -0.65068
0.89398
42 -0.63612
0.729186
43 0.396749
0.965338
44 -0.62566
0.593885
45 -0.43523
-0.04478
46 -0.66307
0.866321
47 -0.75456
-0.03116
48 -0.91128
0.523274
49 -0.88177
0.96148
50 -0.53282
-0.66296
51 -0.34802
0.750813
52 -0.33882
-0.6847
53 0.071458
-0.61145
54 -0.62198
-0.87699
55 0.277614
0.695603
56 0.413396
-0.91809
57 -0.0973
-0.30798
58 -0.89162
0.493541
59 -0.61754
0.132234
60 -0.86174
0.22332
61 0.942456
-0.5973
62 0.787915
-0.62588
63 0.271521
-0.86313
64 0.636426
0.526282
65 -0.48668
0.36336
66 0.124178
0.654574
67 -0.98335
-0.3042
68 0.665858
-0.62011
69 -0.37791
0.828828
70 0.945987
-0.4672
71 0.089622
-0.6889
72 -0.1464
-0.89045
73 0.663226
0.385483
74 0.193837
-0.91153
75 -0.33801
0.479696
76 -0.54719
0.705401
77 -0.1185
-0.13308
78 -0.05487
0.481666
79 -0.66249
0.222822
80 -0.63157
0.822861
81 -0.53281
0.795012
82 -0.73812
-0.67871
83 0.931043
-0.47785
84 -0.50696
-0.76215
85 0.472119
0.537303
86 -0.64921
-0.27739
87 0.871152
0.243021
88 0.135825
-0.20453
89 0.280306
-0.40784
90 0.528771
0.651066
91 0.666711
0.959109
92 -0.87381
-0.87227
93 0.277415
-0.68221
94 0.850749
0.521615
95 -0.88803
0.707438
96 0.920991
0.140835
97 0.249784
0.328697
98 0.029089
-0.08661
99 0.014926
0.697178
100 -0.21558
0.136405
101 -0.40885
0.992437
102 -0.36967
-0.24166
103 -0.13953
-0.12369
104 -0.2792
0.760484
105 -0.05558
0.182796
106 0.407065
0.212775
107 -0.11908
-0.36282
108 -0.77607
0.408583
109 -0.96316
-0.81991
110 0.888927
-0.33517
111 0.209856
0.957904
112 0.655823
-0.89289
113 0.399218
0.119261
114 -0.21277
-0.99069
115 0.131847
0.628239
116 -0.224
-0.42248
117 0.390822
-0.30866
118 0.983395
-0.13172
119 0.322027
-0.34971
120 -0.75704
-0.8989
121 -0.07678
-0.63078
122 0.20301
0.98573
123 -0.07504
-0.38966
124 0.345951
0.677916
125 0.273432
0.017076
126 0.061051
-0.17995
127 0.032153
-0.57838
128 -0.69572
0.908402
129 -0.33637
-0.15768
130 -0.99636
0.792236
131 0.614422
0.417804
132 -0.75441
0.805726
133 -0.16917
-0.91897
134 -0.51806
0.909001
135 0.229715
0.698133
136 -0.67679
0.445494
137 -0.81283
-0.35465
138 0.903847
0.144576
139 -0.23658
0.433991
140 -0.86613
0.294879
141 0.639742
-0.50079
142 0.513531
0.919548
143 0.64073
-0.53262
144 0.225463
0.681082
145 -0.14332
0.099424
146 -0.85626
0.983767
147 -0.66523
0.671427
148 0.131213
-0.43107
149 0.654758
0.080778
150 0.202636
-0.79315
151 0.824304
-0.34999
152 -0.37491
0.119922
153 0.617528
0.861762
154 -0.04594
0.406273
155 0.224994
-0.51244
156 -0.27448
0.456315
157 -0.46562
-0.26531
158 0.70894
-0.39809
159 -0.03779
-0.99151
160 0.652804
-0.65322
161 -0.3714
-0.02051
162 -0.92149
0.637798
163 -0.78861
-0.24897
164 0.516922
-0.52355
165 -0.22161
0.682375
166 -0.96188
-0.02812
167 0.249302
0.838293
168 0.796291
-0.24786
169 0.072501
0.792012
170 0.319628
0.769851
171 0.410343
-0.17406
172 -0.63591
-0.8715
173 0.128656
-0.1152
174 -0.34658
0.712556
175 -0.23302
-0.98016
176 -0.81064
0.880455
177 -0.47934
0.949687
178 -0.90368
-0.24202
179 -0.0681
-0.78752
180 0.351403
-0.48184
181 0.438625
0.644864
182 -0.7432
0.226075
183 -0.96621
-0.04154
184 0.001831
0.741643
185 0.659136
-0.38571
186 0.56686
-0.43974
187 0.291567
-0.50679
188 0.071221
0.622825
189 0.752217
-0.57439
190 -0.70111
-0.05563
191 0.883547
-0.63898
192 -0.96209
-0.88101
193 0.194408
0.946314
194 -0.78689
-0.58902
195 -0.7704
-0.84919
196 0.207707
0.485052
197 0.543697
-0.52322
198 0.777297
-0.10659
199 0.577322
0.075904
200 0.086474
-0.04576
201 -0.78724
-0.08173
202 -0.22384
0.641552
203 -0.32547
-0.82933
204 -0.7839
-0.22219
205 -0.22874
-0.18342
206 0.655936
-0.15162
207 -0.98518
0.241692
208 0.09542
0.010855
209 -0.14169
-0.31474
210 0.535283
-0.94023
211 0.930843
0.871037
212 0.571197
-0.0621
213 -0.97009
-0.0217
214 -0.80929
0.159056
215 -0.49157
0.379003
216 -0.50419
-0.83287
217 -0.44218
0.745661
218 0.50191
0.116854
219 -0.78914
-0.2372
220 0.170037
0.149954
221 -0.81813
-0.13316
222 -0.47689
-0.07521
223 0.822876
-0.51638
224 0.442528
-0.96155
225 -0.62905
0.312424
226 0.459178
0.246618
227 -0.33145
0.919867
228 0.251713
-0.9608
229 -0.94998
0.346151
230 -0.14781
-0.67371
231 -0.13331
0.962925
232 0.347789
0.688469
233 0.34716
-0.45765
234 -0.41232
0.500433
235 0.320995
0.303092
236 0.886138
0.466448
237 0.598878
0.486285
238 0.689002
0.186405
239 -0.87895
-0.54316
240 -0.45789
0.733395
241 0.62069
0.180274
242 0.644396
0.323893
243 0.117053
0.804772
244 0.89505
-0.70493
245 0.640729
-0.42492
246 0.091273
0.534737
247 -0.00673
0.751033
248 0.006751
0.787652
249 -0.54998
0.627215
250 0.301532
0.221804
251 -0.51427
-0.48444
252 -0.79009
-0.39513
253 -0.87753
-0.82692
254 -0.51599
-0.42893
255 0.25731
0.758961
256 -0.78772
-0.30437
257 -0.3135
-0.82033
258 0.168132
-0.12245
259 -0.97477
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260 -0.1498
0.54077
261 -0.77789
-0.44196
262 0.569118
-0.5528
263 0.719659
-0.93094
264 -0.47647
-0.66107
265 0.051783
-0.74414
266 0.558492
-0.09026
267 -0.82765
-0.01828
268 0.08158
0.432166
269 -0.3276
0.113885
270 0.951966
-0.85647
271 0.955461
0.334975
272 0.902427
0.072426
273 0.603154
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274 0.153748
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275 0.365761
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276 -0.65733
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277 -0.90972
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278 0.398513
0.232354
279 0.676635
-0.2586
280 -0.71368
-0.73196
281 0.201711
-0.7344
282 0.461028
-0.60484
283 -0.41661
0.609003
284 0.009749
0.265278
285 -0.82449
0.622357
286 -0.45819
0.185981
287 -0.89046
0.758448
288 0.686577
-0.73563
289 -0.18236
0.983481
290 -0.19401
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291 0.977624
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292 -0.46824
0.449011
293 0.572495
0.359105
294 0.057852
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295 -0.41699
0.513179
296 -0.14302
0.754179
297 -0.85134
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298 -0.47831
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299 -0.59868
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300 -0.35603
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301 0.793919
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303 -0.46081
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304 -0.94025
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305 -0.03983
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313 0.96214
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0.944559
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320 0.193344
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321 0.900417
0.754549
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330 -0.18689
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331 -0.29699
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332 -0.16872
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354 0.167265
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531 0.264847
0.058275
532 0.254228
-0.83247
533 0.793737
-0.98499
534 0.481117
-0.58416
535 -0.54675
-0.60008
536 -0.5331
-0.74613
537 0.253659
0.151158
538 0.066624
-0.46535
539 -0.22003
0.010059
540 -0.78292
0.917236
541 0.522371
0.763185
542 0.245134
0.670542
543 -0.68468
-0.50954
544 0.983081
-0.51281
545 0.817887
0.437016
546 0.459341
0.321471
547 0.6741
0.908393
548 -0.96898
0.76595
549 -0.11049
-0.66312
550 0.787997
-0.53225
551 -0.9779
0.431324
552 0.701776
-0.25727
553 -0.13261
-0.67582
554 0.170165
-0.95232
555 -0.66948
0.238504
556 -0.74866
-0.6812
557 0.715877
0.627792
558 -0.58536
0.008391
559 -0.47681
-0.0204
560 0.993405
-0.42436
561 -0.547
-0.84479
562 0.155702
-0.33403
563 0.528334
-0.50692
564 -0.76742
-0.05733
565 -0.69696
0.225803
566 0.82417
-0.21835
567 0.227017
-0.53029
568 0.631942
-0.37993
569 -0.47996
0.828571
570 0.976874
0.738711
571 0.137279
-0.9415
572 -0.16396
0.76007
573 0.799029
-0.3597
574 0.813962
-0.9285
575 -0.28213
-0.28941
576 0.119831
0.601074
577 -0.76243
0.487847
578 0.302661
0.243891
579 -0.04488
-0.42633
580 0.487289
0.649257
581 0.416876
-0.98393
582 0.797912
0.405747
583 0.466349
-0.40202
584 -0.81348
0.082405
585 0.405058
-0.81847
586 0.67383
-0.55884
587 -0.56997
-0.6598
588 -0.59117
0.576555
589 -0.2475
-0.6193
590 0.66063
-0.1857
591 -0.20833
0.644543
592 -0.98178
-0.0685
593 0.391804
0.067475
594 -0.60271
-0.21681
595 -0.26694
0.562429
596 0.898763
0.63752
597 0.579018
0.868441
598 -0.09561
0.094749
599 0.516371
-0.75027
600 0.315485
-0.9474
601 0.355724
-0.50551
602 0.075431
0.159269
603 -0.95467
0.078278
604 0.396097
0.4695
605 -0.09183
0.973296
606 0.86724
0.436562
607 -0.47864
-0.87729
608 0.898611
-0.8158
609 0.686437
-0.87692
610 0.662089
-0.79693
611 -0.10922
0.207899
612 0.648452
-0.65175
613 0.20297
-0.42931
614 -0.95663
0.608719
615 -0.13902
0.421203
616 -0.37498
-0.81008
617 0.975258
-0.95715
618 0.440291
0.273301
619 0.202123
0.69835
620 0.210533
-0.92625
621 0.518975
-0.61004
622 0.239038
-0.62721
623 -0.73164
0.946397
624 0.636208
-0.92986
625 0.751119
0.55685
626 0.845953
0.337035
627 0.530236
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628 0.82385
0.88654
629 -0.10729
-0.73524
630 -0.56277
-0.41721
631 -0.43183
-0.17366
632 0.068351
-0.65826
633 -0.4493
-0.47583
634 0.861762
-0.56798
635 -0.02659
0.569189
636 -0.98529
0.733448
637 -0.81209
-0.13222
638 0.008233
-0.52402
639 0.09771
0.084094
640 -0.25023
0.534079
641 0.725305
0.225028
642 0.02839
-0.23095
643 -0.71569
0.484093
644 0.771616
0.596866
645 0.927631
-0.50028
646 -0.36475
0.272612
647 0.408929
-0.29768
648 0.424829
0.880698
649 0.804287
-0.17229
650 -0.48817
-0.90184
651 -0.05839
0.31112
652 0.730415
-0.81827
653 -0.88202
-0.27616
654 -0.75726
0.174045
655 0.478525
-0.25676
656 0.903099
-0.35629
657 0.051289
-0.72091
658 -0.26004
0.736858
659 0.341021
-0.73
660 0.400066
0.97054
661 -0.76107
-0.02122
662 -0.87201
-0.64639
663 -0.04039
0.249509
664 -0.16268
-0.40284
665 0.834943
-0.55653
666 -0.5153
-0.10226
667 -0.99022
0.773925
668 -0.64094
-0.69079
669 0.954789
0.822935
670 0.184999
-0.66295
671 0.625127
-0.01973
672 0.57819
-0.35488
673 0.664064
0.334106
674 -0.66992
-0.33098
675 -0.86305
-0.30795
676 -0.924
0.468015
677 -0.49487
-0.36993
678 -0.07128
-0.67438
679 -0.24139
0.077226
680 -0.1606
-0.72405
681 0.762556
-0.73388
682 -0.24573
-0.86389
683 0.449272
0.814623
684 -0.78599
-0.43475
685 0.653665
-0.3287
686 0.070504
-0.81904
687 0.532575
0.634085
688 -0.62445
-0.30393
689 0.619846
0.966659
690 -0.58389
0.499699
691 -0.93529
0.190128
692 0.450315
-0.0528
693 0.265874
0.06851
694 0.595598
0.401792
695 -0.01361
-0.67227
696 -0.64358
-0.88369
697 -0.96001
-0.88323
698 -0.94815
-0.17497
699 0.146149
-0.89433
700 0.423873
0.752597
701 -0.43993
0.968174
702 0.27199
0.096344
703 -0.33146
-0.37322
704 0.140859
0.428495
705 -0.13497
0.566192
706 -0.27531
-0.39204
707 -0.69836
0.676663
708 0.326772
0.642643
709 0.836144
-0.02104
710 0.514621
0.91422
711 -0.64244
0.945255
712 0.689373
0.210215
713 -0.96391
-0.45743
714 -0.96341
0.090872
715 -0.06195
-0.33262
716 -0.13841
-0.5906
717 -0.09553
-0.15537
718 0.850545
0.098335
719 -0.80211
0.512784
720 -0.98597
0.433201
721 -0.15625
-0.28333
722 0.471982
0.047812
723 -0.18948
-0.88933
724 0.928704
0.725272
725 0.073769
0.391973
726 0.282378
-0.12114
727 -0.42551
-0.27111
728 0.650866
-0.00543
729 -0.36407
-0.79388
730 -0.37687
0.090618
731 -0.56081
-0.01873
732 -0.6258
-0.89968
733 0.266718
-0.44851
734 -0.83294
-0.1896
735 -0.5672
-0.52037
736 0.734544
-0.09884
737 0.174154
-0.69552
738 0.195928
-0.32707
739 -0.80578
-0.36512
740 0.416163
-0.86676
741 -0.11251
0.436236
742 -0.69881
0.247235
743 0.707184
0.955982
744 0.937562
-0.45377
745 0.744046
-0.83171
746 0.128948
-0.56236
747 -0.60732
-0.99863
748 -0.09006
0.892113
749 0.101699
-0.74931
750 -0.13619
0.14101
751 0.554341
-0.70133
752 0.702295
0.617894
753 0.294742
-0.05019
754 0.02743
-0.82094
755 -0.74122
-0.32477
756 0.993579
-0.10801
757 0.257589
0.609184
758 -0.92072
-0.20623
759 -0.72609
-0.61405
760 -0.53727
0.985562
761 0.022625
-0.9314
762 -0.98536
-0.65397
763 -0.72201
0.852916
764 0.764153
-0.30726
765 -0.75806
-0.22896
766 -0.06935
0.33307
767 0.786186
0.698415
768 -0.35181
-0.01574
769 0.790746
-0.45851
770 -0.18454
-0.88132
771 0.163133
0.854444
772 0.104235
-0.49295
773 0.927281
0.613781
774 0.801346
-0.6872
775 -0.17929
-0.13726
776 0.550754
-0.1091
777 -0.93083
0.564929
778 -0.54231
0.372403
779 -0.3107
-0.04241
780 -0.11128
-0.26236
781 -0.51283
-0.94263
782 0.939051
-0.0334
783 -0.23784
0.30946
784 0.935336
-0.77011
785 0.113689
0.707402
786 -0.20714
0.762665
787 0.961739
0.018683
788 0.897346
0.257618
789 0.600953
-0.89152
790 0.694716
0.911093
791 0.259365
0.443048
792 -0.34894
0.707657
793 0.462111
-0.61723
794 0.186042
0.86106
795 -0.06533
-0.90156
796 0.964785
-0.09675
797 -0.68014
-0.7605
798 0.005342
-0.10182
799 0.851675
0.246417
800 0.812531
0.0562
801 -0.02271
0.563102
802 0.226198
-0.98495
803 -0.87238
0.265869
804 -0.60135
0.453974
805 -0.15933
-0.09382
806 0.90628
-0.12023
807 0.219591
0.430251
808 0.76024
-0.41752
809 -0.93486
0.273791
810 0.859617
0.049742
811 0.493844
0.80135
812 -0.97163
0.283
813 0.385703
-0.83114
814 0.389122
-0.45633
815 0.228668
0.323512
816 -0.82044
0.714546
817 -0.44153
-0.43383
818 -0.89699
0.928889
819 -0.53981
0.408645
820 -0.54469
0.996927
821 -0.98798
-0.18299
822 -0.26084
0.946135
823 -0.10588
-0.02636
824 -0.11841
-0.80487
825 -0.27148
0.047538
826 -0.66041
0.088696
827 0.582755
0.710216
828 -0.63497
-0.23403
829 -0.54191
0.169448
830 0.637527
-0.2303
831 0.934508
-0.34706
832 -0.29244
-0.39409
833 -0.37632
0.171091
834 -0.4148
0.240645
835 -0.94775
0.162355
836 0.750429
0.111903
837 -0.46408
0.053625
838 -0.75051
0.943111
839 -0.37515
-0.42523
840 0.701521
-0.85191
841 -0.12207
-0.45916
842 -0.70136
0.928923
843 -0.88549
-0.46608
844 0.772809
0.370919
845 0.735724
0.622804
846 0.465452
0.065129
847 -0.18885
0.956983
848 0.37363
-0.30329
849 0.131345
-0.9355
850 -0.16853
0.321882
851 -0.94262
-0.0248
852 -0.91747
-0.92114
853 -0.36382
0.029256
854 0.233361
-0.54852
855 0.298869
-0.913
856 0.485025
-0.69497
857 0.813326
0.321591
858 -0.42765
0.632625
859 0.867967
-0.52161
860 0.311975
0.256629
861 -0.62062
0.752032
862 0.865468
-0.38065
863 0.003622
-0.99894
864 0.75306
-0.11653
865 0.808938
0.475985
866 0.547824
-0.37713
867 -0.62451
-0.84513
868 0.999574
-0.19582
869 -0.85642
0.400202
870 0.989349
0.880363
871 0.935406
0.574415
872 -0.85805
0.765104
873 0.823149
-0.16895
874 -0.70418
0.301481
875 0.728947
0.345182
876 0.509391
0.174456
877 -0.25264
-0.68483
878 -0.34262
0.028715
879 0.765196
0.750012
880 0.113892
-0.83381
881 -0.47483
0.495668
882 -0.85064
0.390084
883 -0.53731
0.614837
884 -0.29659
0.683718
885 -0.33594
0.418555
886 0.903847
-0.33287
887 0.551026
-0.83869
888 -0.58739
0.693332
889 -0.27065
-0.45381
890 -0.8371
0.409135
891 -0.80288
-0.22135
892 -0.16077
-0.87647
893 -0.72645
-0.06198
894 0.295081
0.21519
895 -0.44541
-0.82061
896 0.536523
-0.54006
897 0.199933
-0.74885
898 0.383226
-0.60279
899 -0.29572
-0.06571
900 -0.03503
0.713781
901 -0.08711
-0.24529
902 0.139089
0.792967
903 0.516874
0.540029
904 0.056599
0.072158
905 0.45328
0.833939
906 0.704464
-0.8793
907 -0.57939
0.075621
908 0.800188
0.400431
909 0.71433
0.362621
910 -0.85886
-0.69976
911 0.272852
0.457485
912 -0.05251
0.619186
913 0.965116
-0.50432
914 -0.36512
0.23208
915 0.786643
0.781199
916 0.7819
-0.21889
917 -0.81275
0.212614
918 -0.94548
-0.10767
919 0.518857
0.127745
920 0.16213
0.182454
921 -0.03688
0.982495
922 -0.62301
0.771846
923 0.32703
0.021124
924 -0.24062
0.474989
925 0.960177
-0.18802
926 -0.37055
-0.96247
927 0.766203
-0.47668
928 0.516936
-0.64265
929 0.07847
0.333315
930 0.109338
-0.50708
931 0.184506
0.007448
932 0.781751
0.642497
933 -0.46769
0.073465
934 0.597271
-0.67381
935 -0.86912
-0.655
936 -0.80685
0.351687
937 -0.15468
-0.77038
938 -0.80367
-0.97875
939 0.690167
-0.46254
940 0.518335
-0.35114
941 -0.43699
-0.10526
942 0.172932
-0.74014
943 -0.032
0.390589
944 -0.79737
0.111465
945 0.011076
0.706375
946 -0.62433
-0.89998
947 0.233159
0.653838
948 0.784508
0.026535
949 -0.34703
0.746407
950 0.374112
-0.48756
951 0.971651
0.363107
952 0.027877
0.349901
953 0.289233
0.547148
954 0.602932
0.645428
955 -0.36949
-0.73382
956 0.239264
-0.3949
957 -0.09753
0.229069
958 0.571429
-0.13741
959 0.31967
-0.2172
960 0.531782
0.362739
961 0.734749
0.912163
962 0.14883
-0.64187
963 -0.69179
0.316143
964 0.079675
-0.66311
965 0.501354
0.252218
966 0.749636
0.167086
967 -0.81164
-0.52836
968 -0.45374
0.462335
969 0.530671
-0.48321
970 -0.56643
0.303671
971 0.444448
0.89961
972 0.850256
-0.93006
973 -0.10943
-0.5747
974 -0.53835
0.358838
975 0.098605
-0.56835
976 -0.79394
-0.79596
977 0.065481
0.788517
978 0.203934
-0.34602
979 -0.59325
-0.12475
980 -0.38707
0.683744
981 -0.04714
-0.34171
982 -0.75493
-0.91346
983 0.716259
0.124951
984 -0.63158
-0.01618
985 -0.22135
-0.37901
986 0.245875
-0.19449
987 0.731693
-0.03386
988 -0.27956
0.343105
989 0.115355
-0.61331
990 0.899588
0.776615
991 -0.12771
-0.98093
992 -0.61005
0.873417
993 0.018253
0.160573
994 -0.68128
-0.47131
995 -0.79701
0.539463
996 0.896222
-0.81866
997 0.425502
0.032025
998 0.66468
0.798442
999 -0.05488
-0.03372
1000 -0.7013
-0.29705





Graph of the Points should look something similar to the following: (It might be more shaded depending on the number of points you used.)


After You have Generated 1000 or more Values, you need to separate that values inside the circle from the ones outside of the circle. Basically All you need to do it use the formula X^2 + Y^2 = R^2. Right Next to your X and Y Values column in excel, type =IF( (X^2 + Y^2) < 1,X,0) into the first column and =IF( (X^2 + Y^2) < 1,Y,0) into the second column. This basically means that "If X^2 + Y^2 is less than 1, which means that they are in the circle, then leave that point X or Y else change it to 0, which means that it will be removed from the graph. You can look below to see what you should have by now:







NUMS X
Y X Inside R Y Inside R
1 -0.3753
0.393222 -0.3753 0.393222
2 -0.52305
-0.63836 -0.52305 -0.63836
3 0.645948
-0.09952 0.645948 -0.09952
4 -0.45835
0.530955 -0.45835 0.530955
5 -0.65366
-0.61368 -0.65366 -0.61368
6 0.840407
-0.6665 0 0
7 -0.18093
0.182653 -0.18093 0.182653
8 0.382593
0.837658 0.382593 0.837658
9 0.765181
0.854358 0 0
10 0.784243
-0.96181 0 0
11 0.753266
0.227069 0.753266 0.227069
12 -0.87169
-0.1506 -0.87169 -0.1506
13 -0.4961
0.034662 -0.4961 0.034662
14 -0.13412
-0.96387 -0.13412 -0.96387
15 -0.24221
0.345125 -0.24221 0.345125
16 -0.24996
-0.72305 -0.24996 -0.72305
17 0.417938
-0.20437 0.417938 -0.20437
18 -0.51827
-0.94565 0 0
19 0.412481
-0.67224 0.412481 -0.67224
20 0.831408
0.778381 0 0
21 0.189574
0.234717 0.189574 0.234717
22 -0.91913
0.813221 0 0
23 -0.92543
0.622006 0 0
24 0.7278
-0.21911 0.7278 -0.21911
25 -0.96766
-0.64161 0 0
26 -0.71109
0.565655 -0.71109 0.565655
27 0.955577
0.745066 0 0
28 -0.68654
-0.30849 -0.68654 -0.30849
29 0.339207
0.86824 0.339207 0.86824
30 0.456058
-0.58421 0.456058 -0.58421
31 0.809588
0.198191 0.809588 0.198191
32 0.405219
-0.08023 0.405219 -0.08023
33 -0.9394
-0.79732 0 0
34 0.175434
0.902226 0.175434 0.902226
35 -0.61469
-0.24193 -0.61469 -0.24193
36 0.33836
-0.48176 0.33836 -0.48176
37 -0.5494
-0.39721 -0.5494 -0.39721
38 0.176253
0.816443 0.176253 0.816443
39 -0.32524
-0.23104 -0.32524 -0.23104
40 -0.93887
-0.49109 0 0
41 -0.65068
0.89398 0 0
42 -0.63612
0.729186 -0.63612 0.729186
43 0.396749
0.965338 0 0
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-0.45851 0.790746 -0.45851
770 -0.18454
-0.88132 -0.18454 -0.88132
771 0.163133
0.854444 0.163133 0.854444
772 0.104235
-0.49295 0.104235 -0.49295
773 0.927281
0.613781 0 0
774 0.801346
-0.6872 0 0
775 -0.17929
-0.13726 -0.17929 -0.13726
776 0.550754
-0.1091 0.550754 -0.1091
777 -0.93083
0.564929 0 0
778 -0.54231
0.372403 -0.54231 0.372403
779 -0.3107
-0.04241 -0.3107 -0.04241
780 -0.11128
-0.26236 -0.11128 -0.26236
781 -0.51283
-0.94263 0 0
782 0.939051
-0.0334 0.939051 -0.0334
783 -0.23784
0.30946 -0.23784 0.30946
784 0.935336
-0.77011 0 0
785 0.113689
0.707402 0.113689 0.707402
786 -0.20714
0.762665 -0.20714 0.762665
787 0.961739
0.018683 0.961739 0.018683
788 0.897346
0.257618 0.897346 0.257618
789 0.600953
-0.89152 0 0
790 0.694716
0.911093 0 0
791 0.259365
0.443048 0.259365 0.443048
792 -0.34894
0.707657 -0.34894 0.707657
793 0.462111
-0.61723 0.462111 -0.61723
794 0.186042
0.86106 0.186042 0.86106
795 -0.06533
-0.90156 -0.06533 -0.90156
796 0.964785
-0.09675 0.964785 -0.09675
797 -0.68014
-0.7605 0 0
798 0.005342
-0.10182 0.005342 -0.10182
799 0.851675
0.246417 0.851675 0.246417
800 0.812531
0.0562 0.812531 0.0562
801 -0.02271
0.563102 -0.02271 0.563102
802 0.226198
-0.98495 0 0
803 -0.87238
0.265869 -0.87238 0.265869
804 -0.60135
0.453974 -0.60135 0.453974
805 -0.15933
-0.09382 -0.15933 -0.09382
806 0.90628
-0.12023 0.90628 -0.12023
807 0.219591
0.430251 0.219591 0.430251
808 0.76024
-0.41752 0.76024 -0.41752
809 -0.93486
0.273791 -0.93486 0.273791
810 0.859617
0.049742 0.859617 0.049742
811 0.493844
0.80135 0.493844 0.80135
812 -0.97163
0.283 0 0
813 0.385703
-0.83114 0.385703 -0.83114
814 0.389122
-0.45633 0.389122 -0.45633
815 0.228668
0.323512 0.228668 0.323512
816 -0.82044
0.714546 0 0
817 -0.44153
-0.43383 -0.44153 -0.43383
818 -0.89699
0.928889 0 0
819 -0.53981
0.408645 -0.53981 0.408645
820 -0.54469
0.996927 0 0
821 -0.98798
-0.18299 0 0
822 -0.26084
0.946135 -0.26084 0.946135
823 -0.10588
-0.02636 -0.10588 -0.02636
824 -0.11841
-0.80487 -0.11841 -0.80487
825 -0.27148
0.047538 -0.27148 0.047538
826 -0.66041
0.088696 -0.66041 0.088696
827 0.582755
0.710216 0.582755 0.710216
828 -0.63497
-0.23403 -0.63497 -0.23403
829 -0.54191
0.169448 -0.54191 0.169448
830 0.637527
-0.2303 0.637527 -0.2303
831 0.934508
-0.34706 0.934508 -0.34706
832 -0.29244
-0.39409 -0.29244 -0.39409
833 -0.37632
0.171091 -0.37632 0.171091
834 -0.4148
0.240645 -0.4148 0.240645
835 -0.94775
0.162355 -0.94775 0.162355
836 0.750429
0.111903 0.750429 0.111903
837 -0.46408
0.053625 -0.46408 0.053625
838 -0.75051
0.943111 0 0
839 -0.37515
-0.42523 -0.37515 -0.42523
840 0.701521
-0.85191 0 0
841 -0.12207
-0.45916 -0.12207 -0.45916
842 -0.70136
0.928923 0 0
843 -0.88549
-0.46608 0 0
844 0.772809
0.370919 0.772809 0.370919
845 0.735724
0.622804 0.735724 0.622804
846 0.465452
0.065129 0.465452 0.065129
847 -0.18885
0.956983 -0.18885 0.956983
848 0.37363
-0.30329 0.37363 -0.30329
849 0.131345
-0.9355 0.131345 -0.9355
850 -0.16853
0.321882 -0.16853 0.321882
851 -0.94262
-0.0248 -0.94262 -0.0248
852 -0.91747
-0.92114 0 0
853 -0.36382
0.029256 -0.36382 0.029256
854 0.233361
-0.54852 0.233361 -0.54852
855 0.298869
-0.913 0.298869 -0.913
856 0.485025
-0.69497 0.485025 -0.69497
857 0.813326
0.321591 0.813326 0.321591
858 -0.42765
0.632625 -0.42765 0.632625
859 0.867967
-0.52161 0 0
860 0.311975
0.256629 0.311975 0.256629
861 -0.62062
0.752032 -0.62062 0.752032
862 0.865468
-0.38065 0.865468 -0.38065
863 0.003622
-0.99894 0.003622 -0.99894
864 0.75306
-0.11653 0.75306 -0.11653
865 0.808938
0.475985 0.808938 0.475985
866 0.547824
-0.37713 0.547824 -0.37713
867 -0.62451
-0.84513 0 0
868 0.999574
-0.19582 0 0
869 -0.85642
0.400202 -0.85642 0.400202
870 0.989349
0.880363 0 0
871 0.935406
0.574415 0 0
872 -0.85805
0.765104 0 0
873 0.823149
-0.16895 0.823149 -0.16895
874 -0.70418
0.301481 -0.70418 0.301481
875 0.728947
0.345182 0.728947 0.345182
876 0.509391
0.174456 0.509391 0.174456
877 -0.25264
-0.68483 -0.25264 -0.68483
878 -0.34262
0.028715 -0.34262 0.028715
879 0.765196
0.750012 0 0
880 0.113892
-0.83381 0.113892 -0.83381
881 -0.47483
0.495668 -0.47483 0.495668
882 -0.85064
0.390084 -0.85064 0.390084
883 -0.53731
0.614837 -0.53731 0.614837
884 -0.29659
0.683718 -0.29659 0.683718
885 -0.33594
0.418555 -0.33594 0.418555
886 0.903847
-0.33287 0.903847 -0.33287
887 0.551026
-0.83869 0 0
888 -0.58739
0.693332 -0.58739 0.693332
889 -0.27065
-0.45381 -0.27065 -0.45381
890 -0.8371
0.409135 -0.8371 0.409135
891 -0.80288
-0.22135 -0.80288 -0.22135
892 -0.16077
-0.87647 -0.16077 -0.87647
893 -0.72645
-0.06198 -0.72645 -0.06198
894 0.295081
0.21519 0.295081 0.21519
895 -0.44541
-0.82061 -0.44541 -0.82061
896 0.536523
-0.54006 0.536523 -0.54006
897 0.199933
-0.74885 0.199933 -0.74885
898 0.383226
-0.60279 0.383226 -0.60279
899 -0.29572
-0.06571 -0.29572 -0.06571
900 -0.03503
0.713781 -0.03503 0.713781
901 -0.08711
-0.24529 -0.08711 -0.24529
902 0.139089
0.792967 0.139089 0.792967
903 0.516874
0.540029 0.516874 0.540029
904 0.056599
0.072158 0.056599 0.072158
905 0.45328
0.833939 0.45328 0.833939
906 0.704464
-0.8793 0 0
907 -0.57939
0.075621 -0.57939 0.075621
908 0.800188
0.400431 0.800188 0.400431
909 0.71433
0.362621 0.71433 0.362621
910 -0.85886
-0.69976 0 0
911 0.272852
0.457485 0.272852 0.457485
912 -0.05251
0.619186 -0.05251 0.619186
913 0.965116
-0.50432 0 0
914 -0.36512
0.23208 -0.36512 0.23208
915 0.786643
0.781199 0 0
916 0.7819
-0.21889 0.7819 -0.21889
917 -0.81275
0.212614 -0.81275 0.212614
918 -0.94548
-0.10767 -0.94548 -0.10767
919 0.518857
0.127745 0.518857 0.127745
920 0.16213
0.182454 0.16213 0.182454
921 -0.03688
0.982495 -0.03688 0.982495
922 -0.62301
0.771846 -0.62301 0.771846
923 0.32703
0.021124 0.32703 0.021124
924 -0.24062
0.474989 -0.24062 0.474989
925 0.960177
-0.18802 0.960177 -0.18802
926 -0.37055
-0.96247 0 0
927 0.766203
-0.47668 0.766203 -0.47668
928 0.516936
-0.64265 0.516936 -0.64265
929 0.07847
0.333315 0.07847 0.333315
930 0.109338
-0.50708 0.109338 -0.50708
931 0.184506
0.007448 0.184506 0.007448
932 0.781751
0.642497 0 0
933 -0.46769
0.073465 -0.46769 0.073465
934 0.597271
-0.67381 0.597271 -0.67381
935 -0.86912
-0.655 0 0
936 -0.80685
0.351687 -0.80685 0.351687
937 -0.15468
-0.77038 -0.15468 -0.77038
938 -0.80367
-0.97875 0 0
939 0.690167
-0.46254 0.690167 -0.46254
940 0.518335
-0.35114 0.518335 -0.35114
941 -0.43699
-0.10526 -0.43699 -0.10526
942 0.172932
-0.74014 0.172932 -0.74014
943 -0.032
0.390589 -0.032 0.390589
944 -0.79737
0.111465 -0.79737 0.111465
945 0.011076
0.706375 0.011076 0.706375
946 -0.62433
-0.89998 0 0
947 0.233159
0.653838 0.233159 0.653838
948 0.784508
0.026535 0.784508 0.026535
949 -0.34703
0.746407 -0.34703 0.746407
950 0.374112
-0.48756 0.374112 -0.48756
951 0.971651
0.363107 0 0
952 0.027877
0.349901 0.027877 0.349901
953 0.289233
0.547148 0.289233 0.547148
954 0.602932
0.645428 0.602932 0.645428
955 -0.36949
-0.73382 -0.36949 -0.73382
956 0.239264
-0.3949 0.239264 -0.3949
957 -0.09753
0.229069 -0.09753 0.229069
958 0.571429
-0.13741 0.571429 -0.13741
959 0.31967
-0.2172 0.31967 -0.2172
960 0.531782
0.362739 0.531782 0.362739
961 0.734749
0.912163 0 0
962 0.14883
-0.64187 0.14883 -0.64187
963 -0.69179
0.316143 -0.69179 0.316143
964 0.079675
-0.66311 0.079675 -0.66311
965 0.501354
0.252218 0.501354 0.252218
966 0.749636
0.167086 0.749636 0.167086
967 -0.81164
-0.52836 -0.81164 -0.52836
968 -0.45374
0.462335 -0.45374 0.462335
969 0.530671
-0.48321 0.530671 -0.48321
970 -0.56643
0.303671 -0.56643 0.303671
971 0.444448
0.89961 0 0
972 0.850256
-0.93006 0 0
973 -0.10943
-0.5747 -0.10943 -0.5747
974 -0.53835
0.358838 -0.53835 0.358838
975 0.098605
-0.56835 0.098605 -0.56835
976 -0.79394
-0.79596 0 0
977 0.065481
0.788517 0.065481 0.788517
978 0.203934
-0.34602 0.203934 -0.34602
979 -0.59325
-0.12475 -0.59325 -0.12475
980 -0.38707
0.683744 -0.38707 0.683744
981 -0.04714
-0.34171 -0.04714 -0.34171
982 -0.75493
-0.91346 0 0
983 0.716259
0.124951 0.716259 0.124951
984 -0.63158
-0.01618 -0.63158 -0.01618
985 -0.22135
-0.37901 -0.22135 -0.37901
986 0.245875
-0.19449 0.245875 -0.19449
987 0.731693
-0.03386 0.731693 -0.03386
988 -0.27956
0.343105 -0.27956 0.343105
989 0.115355
-0.61331 0.115355 -0.61331
990 0.899588
0.776615 0 0
991 -0.12771
-0.98093 -0.12771 -0.98093
992 -0.61005
0.873417 0 0
993 0.018253
0.160573 0.018253 0.160573
994 -0.68128
-0.47131 -0.68128 -0.47131
995 -0.79701
0.539463 -0.79701 0.539463
996 0.896222
-0.81866 0 0
997 0.425502
0.032025 0.425502 0.032025
998 0.66468
0.798442 0 0
999 -0.05488
-0.03372 -0.05488 -0.03372
1000 -0.7013
-0.29705 -0.7013 -0.29705









Now you should have the X and Y values that are inside the circle and when you graph them you should something like the following:


 To get the area of the circle and Rectangle type the following in the next column, =IF( (X^2 + Y^2) < 1,1,0) and type =IF( (Xinside^2 + Yinside^2) < 1,1,0), which means that if X^2 + Y^2 or Xinside^2 + Yinside^2 is less than 1 then make X or Y and Xinside and Yinside 1 else 0. Next You have to sum up all the 1's you get for the circle and all the 1's you get for rectangle. See Below to see what you should have by now:








NUMS X
Y X Inside R Y Inside R Area Of C Area of R
1 -0.3753
0.393222 -0.3753 0.393222 1 1
2 -0.52305
-0.63836 -0.52305 -0.63836 1 1
3 0.645948
-0.09952 0.645948 -0.09952 1 1
4 -0.45835
0.530955 -0.45835 0.530955 1 1
5 -0.65366
-0.61368 -0.65366 -0.61368 1 1
6 0.840407
-0.6665 0 0 0 1
7 -0.18093
0.182653 -0.18093 0.182653 1 1
8 0.382593
0.837658 0.382593 0.837658 1 1
9 0.765181
0.854358 0 0 0 1
10 0.784243
-0.96181 0 0 0 1
11 0.753266
0.227069 0.753266 0.227069 1 1
12 -0.87169
-0.1506 -0.87169 -0.1506 1 1
13 -0.4961
0.034662 -0.4961 0.034662 1 1
14 -0.13412
-0.96387 -0.13412 -0.96387 1 1
15 -0.24221
0.345125 -0.24221 0.345125 1 1
16 -0.24996
-0.72305 -0.24996 -0.72305 1 1
17 0.417938
-0.20437 0.417938 -0.20437 1 1
18 -0.51827
-0.94565 0 0 0 1
19 0.412481
-0.67224 0.412481 -0.67224 1 1
20 0.831408
0.778381 0 0 0 1
21 0.189574
0.234717 0.189574 0.234717 1 1
22 -0.91913
0.813221 0 0 0 1
23 -0.92543
0.622006 0 0 0 1
24 0.7278
-0.21911 0.7278 -0.21911 1 1
25 -0.96766
-0.64161 0 0 0 1
26 -0.71109
0.565655 -0.71109 0.565655 1 1
27 0.955577
0.745066 0 0 0 1
28 -0.68654
-0.30849 -0.68654 -0.30849 1 1
29 0.339207
0.86824 0.339207 0.86824 1 1
30 0.456058
-0.58421 0.456058 -0.58421 1 1
31 0.809588
0.198191 0.809588 0.198191 1 1
32 0.405219
-0.08023 0.405219 -0.08023 1 1
33 -0.9394
-0.79732 0 0 0 1
34 0.175434
0.902226 0.175434 0.902226 1 1
35 -0.61469
-0.24193 -0.61469 -0.24193 1 1
36 0.33836
-0.48176 0.33836 -0.48176 1 1
37 -0.5494
-0.39721 -0.5494 -0.39721 1 1
38 0.176253
0.816443 0.176253 0.816443 1 1
39 -0.32524
-0.23104 -0.32524 -0.23104 1 1
40 -0.93887
-0.49109 0 0 0 1
41 -0.65068
0.89398 0 0 0 1
42 -0.63612
0.729186 -0.63612 0.729186 1 1
43 0.396749
0.965338 0 0 0 1
44 -0.62566
0.593885 -0.62566 0.593885 1 1
45 -0.43523
-0.04478 -0.43523 -0.04478 1 1
46 -0.66307
0.866321 0 0 0 1
47 -0.75456
-0.03116 -0.75456 -0.03116 1 1
48 -0.91128
0.523274 0 0 0 1
49 -0.88177
0.96148 0 0 0 1
50 -0.53282
-0.66296 -0.53282 -0.66296 1 1
51 -0.34802
0.750813 -0.34802 0.750813 1 1
52 -0.33882
-0.6847 -0.33882 -0.6847 1 1
53 0.071458
-0.61145 0.071458 -0.61145 1 1
54 -0.62198
-0.87699 0 0 0 1
55 0.277614
0.695603 0.277614 0.695603 1 1
56 0.413396
-0.91809 0 0 0 1
57 -0.0973
-0.30798 -0.0973 -0.30798 1 1
58 -0.89162
0.493541 0 0 0 1
59 -0.61754
0.132234 -0.61754 0.132234 1 1
60 -0.86174
0.22332 -0.86174 0.22332 1 1
61 0.942456
-0.5973 0 0 0 1
62 0.787915
-0.62588 0 0 0 1
63 0.271521
-0.86313 0.271521 -0.86313 1 1
64 0.636426
0.526282 0.636426 0.526282 1 1
65 -0.48668
0.36336 -0.48668 0.36336 1 1
66 0.124178
0.654574 0.124178 0.654574 1 1
67 -0.98335
-0.3042 0 0 0 1
68 0.665858
-0.62011 0.665858 -0.62011 1 1
69 -0.37791
0.828828 -0.37791 0.828828 1 1
70 0.945987
-0.4672 0 0 0 1
71 0.089622
-0.6889 0.089622 -0.6889 1 1
72 -0.1464
-0.89045 -0.1464 -0.89045 1 1
73 0.663226
0.385483 0.663226 0.385483 1 1
74 0.193837
-0.91153 0.193837 -0.91153 1 1
75 -0.33801
0.479696 -0.33801 0.479696 1 1
76 -0.54719
0.705401 -0.54719 0.705401 1 1
77 -0.1185
-0.13308 -0.1185 -0.13308 1 1
78 -0.05487
0.481666 -0.05487 0.481666 1 1
79 -0.66249
0.222822 -0.66249 0.222822 1 1
80 -0.63157
0.822861 0 0 0 1
81 -0.53281
0.795012 -0.53281 0.795012 1 1
82 -0.73812
-0.67871 0 0 0 1
83 0.931043
-0.47785 0 0 0 1
84 -0.50696
-0.76215 -0.50696 -0.76215 1 1
85 0.472119
0.537303 0.472119 0.537303 1 1
86 -0.64921
-0.27739 -0.64921 -0.27739 1 1
87 0.871152
0.243021 0.871152 0.243021 1 1
88 0.135825
-0.20453 0.135825 -0.20453 1 1
89 0.280306
-0.40784 0.280306 -0.40784 1 1
90 0.528771
0.651066 0.528771 0.651066 1 1
91 0.666711
0.959109 0 0 0 1
92 -0.87381
-0.87227 0 0 0 1
93 0.277415
-0.68221 0.277415 -0.68221 1 1
94 0.850749
0.521615 0.850749 0.521615 1 1
95 -0.88803
0.707438 0 0 0 1
96 0.920991
0.140835 0.920991 0.140835 1 1
97 0.249784
0.328697 0.249784 0.328697 1 1
98 0.029089
-0.08661 0.029089 -0.08661 1 1
99 0.014926
0.697178 0.014926 0.697178 1 1
100 -0.21558
0.136405 -0.21558 0.136405 1 1
101 -0.40885
0.992437 0 0 0 1
102 -0.36967
-0.24166 -0.36967 -0.24166 1 1
103 -0.13953
-0.12369 -0.13953 -0.12369 1 1
104 -0.2792
0.760484 -0.2792 0.760484 1 1
105 -0.05558
0.182796 -0.05558 0.182796 1 1
106 0.407065
0.212775 0.407065 0.212775 1 1
107 -0.11908
-0.36282 -0.11908 -0.36282 1 1
108 -0.77607
0.408583 -0.77607 0.408583 1 1
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-0.6872 0 0 0 1
775 -0.17929
-0.13726 -0.17929 -0.13726 1 1
776 0.550754
-0.1091 0.550754 -0.1091 1 1
777 -0.93083
0.564929 0 0 0 1
778 -0.54231
0.372403 -0.54231 0.372403 1 1
779 -0.3107
-0.04241 -0.3107 -0.04241 1 1
780 -0.11128
-0.26236 -0.11128 -0.26236 1 1
781 -0.51283
-0.94263 0 0 0 1
782 0.939051
-0.0334 0.939051 -0.0334 1 1
783 -0.23784
0.30946 -0.23784 0.30946 1 1
784 0.935336
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785 0.113689
0.707402 0.113689 0.707402 1 1
786 -0.20714
0.762665 -0.20714 0.762665 1 1
787 0.961739
0.018683 0.961739 0.018683 1 1
788 0.897346
0.257618 0.897346 0.257618 1 1
789 0.600953
-0.89152 0 0 0 1
790 0.694716
0.911093 0 0 0 1
791 0.259365
0.443048 0.259365 0.443048 1 1
792 -0.34894
0.707657 -0.34894 0.707657 1 1
793 0.462111
-0.61723 0.462111 -0.61723 1 1
794 0.186042
0.86106 0.186042 0.86106 1 1
795 -0.06533
-0.90156 -0.06533 -0.90156 1 1
796 0.964785
-0.09675 0.964785 -0.09675 1 1
797 -0.68014
-0.7605 0 0 0 1
798 0.005342
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799 0.851675
0.246417 0.851675 0.246417 1 1
800 0.812531
0.0562 0.812531 0.0562 1 1
801 -0.02271
0.563102 -0.02271 0.563102 1 1
802 0.226198
-0.98495 0 0 0 1
803 -0.87238
0.265869 -0.87238 0.265869 1 1
804 -0.60135
0.453974 -0.60135 0.453974 1 1
805 -0.15933
-0.09382 -0.15933 -0.09382 1 1
806 0.90628
-0.12023 0.90628 -0.12023 1 1
807 0.219591
0.430251 0.219591 0.430251 1 1
808 0.76024
-0.41752 0.76024 -0.41752 1 1
809 -0.93486
0.273791 -0.93486 0.273791 1 1
810 0.859617
0.049742 0.859617 0.049742 1 1
811 0.493844
0.80135 0.493844 0.80135 1 1
812 -0.97163
0.283 0 0 0 1
813 0.385703
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814 0.389122
-0.45633 0.389122 -0.45633 1 1
815 0.228668
0.323512 0.228668 0.323512 1 1
816 -0.82044
0.714546 0 0 0 1
817 -0.44153
-0.43383 -0.44153 -0.43383 1 1
818 -0.89699
0.928889 0 0 0 1
819 -0.53981
0.408645 -0.53981 0.408645 1 1
820 -0.54469
0.996927 0 0 0 1
821 -0.98798
-0.18299 0 0 0 1
822 -0.26084
0.946135 -0.26084 0.946135 1 1
823 -0.10588
-0.02636 -0.10588 -0.02636 1 1
824 -0.11841
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825 -0.27148
0.047538 -0.27148 0.047538 1 1
826 -0.66041
0.088696 -0.66041 0.088696 1 1
827 0.582755
0.710216 0.582755 0.710216 1 1
828 -0.63497
-0.23403 -0.63497 -0.23403 1 1
829 -0.54191
0.169448 -0.54191 0.169448 1 1
830 0.637527
-0.2303 0.637527 -0.2303 1 1
831 0.934508
-0.34706 0.934508 -0.34706 1 1
832 -0.29244
-0.39409 -0.29244 -0.39409 1 1
833 -0.37632
0.171091 -0.37632 0.171091 1 1
834 -0.4148
0.240645 -0.4148 0.240645 1 1
835 -0.94775
0.162355 -0.94775 0.162355 1 1
836 0.750429
0.111903 0.750429 0.111903 1 1
837 -0.46408
0.053625 -0.46408 0.053625 1 1
838 -0.75051
0.943111 0 0 0 1
839 -0.37515
-0.42523 -0.37515 -0.42523 1 1
840 0.701521
-0.85191 0 0 0 1
841 -0.12207
-0.45916 -0.12207 -0.45916 1 1
842 -0.70136
0.928923 0 0 0 1
843 -0.88549
-0.46608 0 0 0 1
844 0.772809
0.370919 0.772809 0.370919 1 1
845 0.735724
0.622804 0.735724 0.622804 1 1
846 0.465452
0.065129 0.465452 0.065129 1 1
847 -0.18885
0.956983 -0.18885 0.956983 1 1
848 0.37363
-0.30329 0.37363 -0.30329 1 1
849 0.131345
-0.9355 0.131345 -0.9355 1 1
850 -0.16853
0.321882 -0.16853 0.321882 1 1
851 -0.94262
-0.0248 -0.94262 -0.0248 1 1
852 -0.91747
-0.92114 0 0 0 1
853 -0.36382
0.029256 -0.36382 0.029256 1 1
854 0.233361
-0.54852 0.233361 -0.54852 1 1
855 0.298869
-0.913 0.298869 -0.913 1 1
856 0.485025
-0.69497 0.485025 -0.69497 1 1
857 0.813326
0.321591 0.813326 0.321591 1 1
858 -0.42765
0.632625 -0.42765 0.632625 1 1
859 0.867967
-0.52161 0 0 0 1
860 0.311975
0.256629 0.311975 0.256629 1 1
861 -0.62062
0.752032 -0.62062 0.752032 1 1
862 0.865468
-0.38065 0.865468 -0.38065 1 1
863 0.003622
-0.99894 0.003622 -0.99894 1 1
864 0.75306
-0.11653 0.75306 -0.11653 1 1
865 0.808938
0.475985 0.808938 0.475985 1 1
866 0.547824
-0.37713 0.547824 -0.37713 1 1
867 -0.62451
-0.84513 0 0 0 1
868 0.999574
-0.19582 0 0 0 1
869 -0.85642
0.400202 -0.85642 0.400202 1 1
870 0.989349
0.880363 0 0 0 1
871 0.935406
0.574415 0 0 0 1
872 -0.85805
0.765104 0 0 0 1
873 0.823149
-0.16895 0.823149 -0.16895 1 1
874 -0.70418
0.301481 -0.70418 0.301481 1 1
875 0.728947
0.345182 0.728947 0.345182 1 1
876 0.509391
0.174456 0.509391 0.174456 1 1
877 -0.25264
-0.68483 -0.25264 -0.68483 1 1
878 -0.34262
0.028715 -0.34262 0.028715 1 1
879 0.765196
0.750012 0 0 0 1
880 0.113892
-0.83381 0.113892 -0.83381 1 1
881 -0.47483
0.495668 -0.47483 0.495668 1 1
882 -0.85064
0.390084 -0.85064 0.390084 1 1
883 -0.53731
0.614837 -0.53731 0.614837 1 1
884 -0.29659
0.683718 -0.29659 0.683718 1 1
885 -0.33594
0.418555 -0.33594 0.418555 1 1
886 0.903847
-0.33287 0.903847 -0.33287 1 1
887 0.551026
-0.83869 0 0 0 1
888 -0.58739
0.693332 -0.58739 0.693332 1 1
889 -0.27065
-0.45381 -0.27065 -0.45381 1 1
890 -0.8371
0.409135 -0.8371 0.409135 1 1
891 -0.80288
-0.22135 -0.80288 -0.22135 1 1
892 -0.16077
-0.87647 -0.16077 -0.87647 1 1
893 -0.72645
-0.06198 -0.72645 -0.06198 1 1
894 0.295081
0.21519 0.295081 0.21519 1 1
895 -0.44541
-0.82061 -0.44541 -0.82061 1 1
896 0.536523
-0.54006 0.536523 -0.54006 1 1
897 0.199933
-0.74885 0.199933 -0.74885 1 1
898 0.383226
-0.60279 0.383226 -0.60279 1 1
899 -0.29572
-0.06571 -0.29572 -0.06571 1 1
900 -0.03503
0.713781 -0.03503 0.713781 1 1
901 -0.08711
-0.24529 -0.08711 -0.24529 1 1
902 0.139089
0.792967 0.139089 0.792967 1 1
903 0.516874
0.540029 0.516874 0.540029 1 1
904 0.056599
0.072158 0.056599 0.072158 1 1
905 0.45328
0.833939 0.45328 0.833939 1 1
906 0.704464
-0.8793 0 0 0 1
907 -0.57939
0.075621 -0.57939 0.075621 1 1
908 0.800188
0.400431 0.800188 0.400431 1 1
909 0.71433
0.362621 0.71433 0.362621 1 1
910 -0.85886
-0.69976 0 0 0 1
911 0.272852
0.457485 0.272852 0.457485 1 1
912 -0.05251
0.619186 -0.05251 0.619186 1 1
913 0.965116
-0.50432 0 0 0 1
914 -0.36512
0.23208 -0.36512 0.23208 1 1
915 0.786643
0.781199 0 0 0 1
916 0.7819
-0.21889 0.7819 -0.21889 1 1
917 -0.81275
0.212614 -0.81275 0.212614 1 1
918 -0.94548
-0.10767 -0.94548 -0.10767 1 1
919 0.518857
0.127745 0.518857 0.127745 1 1
920 0.16213
0.182454 0.16213 0.182454 1 1
921 -0.03688
0.982495 -0.03688 0.982495 1 1
922 -0.62301
0.771846 -0.62301 0.771846 1 1
923 0.32703
0.021124 0.32703 0.021124 1 1
924 -0.24062
0.474989 -0.24062 0.474989 1 1
925 0.960177
-0.18802 0.960177 -0.18802 1 1
926 -0.37055
-0.96247 0 0 0 1
927 0.766203
-0.47668 0.766203 -0.47668 1 1
928 0.516936
-0.64265 0.516936 -0.64265 1 1
929 0.07847
0.333315 0.07847 0.333315 1 1
930 0.109338
-0.50708 0.109338 -0.50708 1 1
931 0.184506
0.007448 0.184506 0.007448 1 1
932 0.781751
0.642497 0 0 0 1
933 -0.46769
0.073465 -0.46769 0.073465 1 1
934 0.597271
-0.67381 0.597271 -0.67381 1 1
935 -0.86912
-0.655 0 0 0 1
936 -0.80685
0.351687 -0.80685 0.351687 1 1
937 -0.15468
-0.77038 -0.15468 -0.77038 1 1
938 -0.80367
-0.97875 0 0 0 1
939 0.690167
-0.46254 0.690167 -0.46254 1 1
940 0.518335
-0.35114 0.518335 -0.35114 1 1
941 -0.43699
-0.10526 -0.43699 -0.10526 1 1
942 0.172932
-0.74014 0.172932 -0.74014 1 1
943 -0.032
0.390589 -0.032 0.390589 1 1
944 -0.79737
0.111465 -0.79737 0.111465 1 1
945 0.011076
0.706375 0.011076 0.706375 1 1
946 -0.62433
-0.89998 0 0 0 1
947 0.233159
0.653838 0.233159 0.653838 1 1
948 0.784508
0.026535 0.784508 0.026535 1 1
949 -0.34703
0.746407 -0.34703 0.746407 1 1
950 0.374112
-0.48756 0.374112 -0.48756 1 1
951 0.971651
0.363107 0 0 0 1
952 0.027877
0.349901 0.027877 0.349901 1 1
953 0.289233
0.547148 0.289233 0.547148 1 1
954 0.602932
0.645428 0.602932 0.645428 1 1
955 -0.36949
-0.73382 -0.36949 -0.73382 1 1
956 0.239264
-0.3949 0.239264 -0.3949 1 1
957 -0.09753
0.229069 -0.09753 0.229069 1 1
958 0.571429
-0.13741 0.571429 -0.13741 1 1
959 0.31967
-0.2172 0.31967 -0.2172 1 1
960 0.531782
0.362739 0.531782 0.362739 1 1
961 0.734749
0.912163 0 0 0 1
962 0.14883
-0.64187 0.14883 -0.64187 1 1
963 -0.69179
0.316143 -0.69179 0.316143 1 1
964 0.079675
-0.66311 0.079675 -0.66311 1 1
965 0.501354
0.252218 0.501354 0.252218 1 1
966 0.749636
0.167086 0.749636 0.167086 1 1
967 -0.81164
-0.52836 -0.81164 -0.52836 1 1
968 -0.45374
0.462335 -0.45374 0.462335 1 1
969 0.530671
-0.48321 0.530671 -0.48321 1 1
970 -0.56643
0.303671 -0.56643 0.303671 1 1
971 0.444448
0.89961 0 0 0 1
972 0.850256
-0.93006 0 0 0 1
973 -0.10943
-0.5747 -0.10943 -0.5747 1 1
974 -0.53835
0.358838 -0.53835 0.358838 1 1
975 0.098605
-0.56835 0.098605 -0.56835 1 1
976 -0.79394
-0.79596 0 0 0 1
977 0.065481
0.788517 0.065481 0.788517 1 1
978 0.203934
-0.34602 0.203934 -0.34602 1 1
979 -0.59325
-0.12475 -0.59325 -0.12475 1 1
980 -0.38707
0.683744 -0.38707 0.683744 1 1
981 -0.04714
-0.34171 -0.04714 -0.34171 1 1
982 -0.75493
-0.91346 0 0 0 1
983 0.716259
0.124951 0.716259 0.124951 1 1
984 -0.63158
-0.01618 -0.63158 -0.01618 1 1
985 -0.22135
-0.37901 -0.22135 -0.37901 1 1
986 0.245875
-0.19449 0.245875 -0.19449 1 1
987 0.731693
-0.03386 0.731693 -0.03386 1 1
988 -0.27956
0.343105 -0.27956 0.343105 1 1
989 0.115355
-0.61331 0.115355 -0.61331 1 1
990 0.899588
0.776615 0 0 0 1
991 -0.12771
-0.98093 -0.12771 -0.98093 1 1
992 -0.61005
0.873417 0 0 0 1
993 0.018253
0.160573 0.018253 0.160573 1 1
994 -0.68128
-0.47131 -0.68128 -0.47131 1 1
995 -0.79701
0.539463 -0.79701 0.539463 1 1
996 0.896222
-0.81866 0 0 0 1
997 0.425502
0.032025 0.425502 0.032025 1 1
998 0.66468
0.798442 0 0 0 1
999 -0.05488
-0.03372 -0.05488 -0.03372 1 1
1000 -0.7013
-0.29705 -0.7013 -0.29705 1 1









Once I've summed up all the 1's I got 775 for the area of the circle and obviously 1000 for the area of the rectangle since I used 1000 random points. To get the value for Pi, you have divide the area of the circle by the number of tries and then multiple by 4. (775/1000)*4 and I got 3.09 which is very close to 3.14, like I said the more values you use for X and Y, the closer you will get to value of Pi. And Every time you refresh or double click any cell, the random numbers will change and give another value close to Pi.

Thank you for reading, You can ask anything you want or any questions in the comments.

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