title
Coding Challenge 95: Approximating the Value of Pi
description
In this coding challenge, I use use a "monte carlo" method to approximate the value of Pi in Processing (Java). Code: https://thecodingtrain.com/challenges/95-approximating-the-value-of-pi
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References:
đĨ§ Million Pi Digits: http://www.piday.org/million/
Videos:
đĨ STEMcoding celebrates Pi day!: https://www.youtube.com/playlist?list=PLISRe8GegO8TbpZK2qvOi6y0kphRI-3xw
đ Learning Processing: https://www.youtube.com/playlist?list=PLRqwX-V7Uu6ZYJC7L-r6rX6utt6wwJCyi
đ´ Coding Train Live 126.1: https://youtu.be/BOk4Dl-gw14?t=1565s
Related Coding Challenges:
đ #96 Visualizing the Digits of Pi: https://youtu.be/WEd_UIKG-uc
đ #140 Leibniz Formula for Pi: https://youtu.be/uH4trBNn540
đ #156 Peeking Inside Pi: https://youtu.be/MEdpRYyjz_0
đ #161 Estimating Ī from Random Numbers with Euclid's Algorithm: https://youtu.be/EvS_a921dBo
đ #169 Pi in the Sky Game: https://youtu.be/_H9JIwWP7HQ
Timestamps:
0:00 Approximating PI
0:48 Suggestion from akraus53
1:43 Methodology
7:31 Let's code!
13:30 Determine number of "darts" in the circle
18:20 Casting to doubles to increase precision
22:07 Keep track of current best estimate
26:30 Suggestions and conclusion
Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound
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This description was auto-generated. If you see a problem, please open an issue: https://github.com/CodingTrain/thecodingtrain.com/issues/new
#montecarlo #estimatingpi #processing
detail
{'title': 'Coding Challenge 95: Approximating the Value of Pi', 'heatmap': [{'end': 1508.199, 'start': 1488.228, 'weight': 1}], 'summary': 'Explores approximating the value of pi through methods like random particles, dart-throwing simulation, and precision calculations using float and double data types in java, aiming to improve accuracy and efficiency in approximations.', 'chapters': [{'end': 84.411, 'segs': [{'end': 84.411, 'src': 'embed', 'start': 22.256, 'weight': 0, 'content': [{'end': 27.498, 'text': 'You can go and compare it to pi-day.org slash million, which I think has the first million digits of pi.', 'start': 22.256, 'duration': 5.242}, {'end': 32.96, 'text': 'But this is a processing sketch using a particular algorithm to calculate all the digits of pi one at a time.', 'start': 27.678, 'duration': 5.282}, {'end': 34.62, 'text': 'It will go on forever.', 'start': 33.32, 'duration': 1.3}, {'end': 37.281, 'text': 'It will get very, very, very slow pretty quickly.', 'start': 34.82, 'duration': 2.461}, {'end': 39.602, 'text': 'I will come back to this in a future video.', 'start': 37.301, 'duration': 2.301}, {'end': 44.584, 'text': "But what I'm going to do in this video is look at a way to approximate the value of pi.", 'start': 39.802, 'duration': 4.782}, {'end': 46.485, 'text': 'Now, this came in as a suggestion.', 'start': 44.624, 'duration': 1.861}, {'end': 56.451, 'text': 'from originally from a Krauss53 on GitHub for how to look at random particles that end up in a circle or outside of a circle.', 'start': 47.305, 'duration': 9.146}, {'end': 59.933, 'text': "Interesting That's something to do with the area of the circle.", 'start': 56.691, 'duration': 3.242}, {'end': 61.434, 'text': "So I'm going to diagram this out.", 'start': 60.013, 'duration': 1.421}, {'end': 71.981, 'text': 'I should also mention thank you to the STEM coding YouTube channel and a STEM coding project, which has a ton of videos in various topics,', 'start': 61.474, 'duration': 10.507}, {'end': 76.284, 'text': 'using programming and coding to teach different types of STEM-related topics.', 'start': 71.981, 'duration': 4.303}, {'end': 76.765, 'text': "It's wonderful.", 'start': 76.344, 'duration': 0.421}, {'end': 77.585, 'text': 'They have a video.', 'start': 76.805, 'duration': 0.78}, {'end': 80.167, 'text': "You can find a link to it in this video's description.", 'start': 77.605, 'duration': 2.562}, {'end': 82.929, 'text': "Basically doing exactly the same thing that I'm about to try to do.", 'start': 80.487, 'duration': 2.442}, {'end': 84.411, 'text': 'Probably better.', 'start': 83.57, 'duration': 0.841}], 'summary': 'Processing sketch calculates pi, while video explores pi approximation using random particles in circle.', 'duration': 62.155, 'max_score': 22.256, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q22256.jpg'}], 'start': 2.416, 'title': 'Approximating pi with random particles', 'summary': 'Explores the process of approximating the value of pi using a coding challenge, comparing it to the actual number of pi, and mentioning a stem coding youtube channel and project. it also discusses a suggestion on how to look at random particles that end up in a circle or outside of a circle to approximate the value of pi.', 'chapters': [{'end': 84.411, 'start': 2.416, 'title': 'Approximating pi with random particles', 'summary': 'Explores the process of approximating the value of pi using a coding challenge, comparing it to the actual number of pi, and mentioning a stem coding youtube channel and project. the chapter also discusses a suggestion on how to look at random particles that end up in a circle or outside of a circle to approximate the value of pi.', 'duration': 81.995, 'highlights': ['The chapter explores the process of approximating the value of pi using a coding challenge The speaker discusses a coding challenge to approximate the value of pi, showcasing a processing sketch using a particular algorithm to calculate all the digits of pi one at a time.', 'Comparing the approximation to the actual number of pi The speaker mentions the existence of the actual number pi and suggests fact-checking it by comparing it to pi-day.org/slash million, which supposedly has the first million digits of pi.', 'Acknowledgment of a STEM coding YouTube channel and project The speaker expresses gratitude to the STEM coding YouTube channel and project, highlighting its numerous videos covering various STEM-related topics using programming and coding for teaching purposes.', 'Discussion of a suggestion related to approximating pi with random particles The chapter mentions a suggestion from a GitHub user on how to use random particles that end up in a circle or outside of a circle to approximate the value of pi.']}], 'duration': 81.995, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q2416.jpg', 'highlights': ['The speaker discusses a coding challenge to approximate the value of pi, showcasing a processing sketch using a particular algorithm to calculate all the digits of pi one at a time.', 'The chapter mentions a suggestion from a GitHub user on how to use random particles that end up in a circle or outside of a circle to approximate the value of pi.', 'The speaker mentions the existence of the actual number pi and suggests fact-checking it by comparing it to pi-day.org/slash million, which supposedly has the first million digits of pi.', 'The speaker expresses gratitude to the STEM coding YouTube channel and project, highlighting its numerous videos covering various STEM-related topics using programming and coding for teaching purposes.']}, {'end': 456.359, 'segs': [{'end': 163.101, 'src': 'embed', 'start': 135.26, 'weight': 2, 'content': [{'end': 137.582, 'text': 'This is the formula for the circumference of a circle.', 'start': 135.26, 'duration': 2.322}, {'end': 141.766, 'text': 'Now, what are these things? Well, 2 is the number 2.', 'start': 137.642, 'duration': 4.124}, {'end': 143.147, 'text': 'r refers to the radius.', 'start': 141.766, 'duration': 1.381}, {'end': 146.557, 'text': 'center to the edge, r.', 'start': 144.657, 'duration': 1.9}, {'end': 150.438, 'text': 'This is the same length anywhere from the center of the circle to any edge point.', 'start': 146.557, 'duration': 3.881}, {'end': 156.72, 'text': 'And pi, well, this is this sort of magic number, 3.1415926.', 'start': 150.778, 'duration': 5.942}, {'end': 160.78, 'text': "That's all I can remember.", 'start': 156.72, 'duration': 4.06}, {'end': 163.101, 'text': 'I might not have gotten the 2 and the 6 right.', 'start': 160.8, 'duration': 2.301}], 'summary': 'Formula for circle circumference: 2Īr, where Ī is approximately 3.1415926.', 'duration': 27.841, 'max_score': 135.26, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q135260.jpg'}, {'end': 307.987, 'src': 'embed', 'start': 279.401, 'weight': 1, 'content': [{'end': 280.862, 'text': '4r squared, pi r squared.', 'start': 279.401, 'duration': 1.461}, {'end': 281.923, 'text': 'Now imagine something.', 'start': 280.902, 'duration': 1.021}, {'end': 291.65, 'text': "There's a relationship here, right? There's a relationship between the area of a, let's say the area of the circle to the area of the square.", 'start': 283.464, 'duration': 8.186}, {'end': 294.652, 'text': 'That relationship can be expressed as a ratio.', 'start': 292.331, 'duration': 2.321}, {'end': 301.938, 'text': 'I could say the area of the circle, pi r squared, to the area of the square, 4r squared.', 'start': 295.713, 'duration': 6.225}, {'end': 303.959, 'text': "The r's cancel out.", 'start': 302.798, 'duration': 1.161}, {'end': 307.987, 'text': 'The ratio is pi divided by 4.', 'start': 303.999, 'duration': 3.988}], 'summary': 'The area of a circle to a square is in a ratio of pi to 4.', 'duration': 28.586, 'max_score': 279.401, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q279401.jpg'}, {'end': 397.919, 'src': 'embed', 'start': 362.107, 'weight': 0, 'content': [{'end': 364.569, 'text': 'divided by the number of darts that have landed in the square.', 'start': 362.107, 'duration': 2.462}, {'end': 368.052, 'text': 'Now three have landed in the circle and four have landed in the square.', 'start': 364.669, 'duration': 3.383}, {'end': 386.386, 'text': 'So I could say pi, in this case pi is approximately four times the circle count divided by the square count which is equal to 3 divided by 4.', 'start': 368.712, 'duration': 17.674}, {'end': 390.573, 'text': '4 times 3 divided by 4 is what? 3.', 'start': 386.386, 'duration': 4.187}, {'end': 397.079, 'text': 'So there is my approximation of pi, 3.0.', 'start': 390.573, 'duration': 6.506}, {'end': 397.919, 'text': "So that's right.", 'start': 397.079, 'duration': 0.84}], 'summary': 'Approximation of pi as 3.0 using dart experiment', 'duration': 35.812, 'max_score': 362.107, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q362107.jpg'}], 'start': 85.191, 'title': 'Approximating pi methods', 'summary': 'Explores two methods for approximating the value of pi, one based on the circumference of a circle and another using a dart-throwing simulation, aiming to improve the approximation of pi with quantifiable data and methods.', 'chapters': [{'end': 223.242, 'start': 85.191, 'title': 'Approximating pi using circumference', 'summary': 'Delves into approximating the digits of pi using the formula for the circumference of a circle and proposes a method to calculate the number pi based on measuring the circumference and the value of radius.', 'duration': 138.051, 'highlights': ['The chapter delves into approximating the digits of pi using the formula for the circumference of a circle and proposes a method to calculate the number pi based on measuring the circumference and the value of radius. The chapter discusses approximating the digits of pi using the formula for the circumference of a circle and proposes a method to calculate the number pi based on measuring the circumference and the value of radius.', 'The formula for the circumference of a circle is explained as 2 pi r, where 2 is the number 2, r refers to the radius, and pi is approximately 3.1415926. The formula for the circumference of a circle is explained as 2 pi r, where 2 is the number 2, r refers to the radius, and pi is approximately 3.1415926.', 'The discussion also touches on the relationship between pi and tau, where tau is 2 pi, and how it can be used to simplify the calculation of circumference. The discussion also touches on the relationship between pi and tau, where tau is 2 pi, and how it can be used to simplify the calculation of circumference.']}, {'end': 456.359, 'start': 223.482, 'title': 'Approximating pi with dart throwing', 'summary': 'Discusses using the ratio of the area of a circle to the area of a square to approximate the number pi using a dart-throwing simulation, with an initial approximation of 3.0 based on 4 darts, aiming to get closer to the actual value of pi with more darts.', 'duration': 232.877, 'highlights': ['The ratio of the area of a circle to the area of a square can be expressed as a ratio, pi r squared to 4r squared, with the ratio simplifying to pi divided by 4.', 'The dart-throwing simulation approximates pi as 4 times the circle count divided by the square count, yielding an initial approximation of 3.0 based on 4 darts, with the potential for a better approximation with more darts.', 'The use of a pseudo random number generator for dart throwing is considered as a potential approach, providing a topic for further exploration in the implementation of the simulation.']}], 'duration': 371.168, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q85191.jpg', 'highlights': ['The dart-throwing simulation approximates pi as 4 times the circle count divided by the square count, yielding an initial approximation of 3.0 based on 4 darts, with the potential for a better approximation with more darts.', 'The ratio of the area of a circle to the area of a square can be expressed as a ratio, pi r squared to 4r squared, with the ratio simplifying to pi divided by 4.', 'The formula for the circumference of a circle is explained as 2 pi r, where 2 is the number 2, r refers to the radius, and pi is approximately 3.1415926.']}, {'end': 777.492, 'segs': [{'end': 485.771, 'src': 'embed', 'start': 456.379, 'weight': 0, 'content': [{'end': 457.903, 'text': "And I'm going to go to a blank sketch.", 'start': 456.379, 'duration': 1.524}, {'end': 461.371, 'text': "Whoops, I'm actually just going to close this.", 'start': 459.229, 'duration': 2.142}, {'end': 464.173, 'text': "And I'm going to go to a blank sketch.", 'start': 463.112, 'duration': 1.061}, {'end': 470.438, 'text': "OK, so what are the first things that I need to do? Let's create a window that's 400 by 400.", 'start': 464.293, 'duration': 6.145}, {'end': 473.061, 'text': "Let's give it a background of 0.", 'start': 470.438, 'duration': 2.623}, {'end': 473.981, 'text': "Yeah, 0, that's fine.", 'start': 473.061, 'duration': 0.92}, {'end': 476.624, 'text': 'Stroke 255.', 'start': 474.682, 'duration': 1.942}, {'end': 478.205, 'text': "Then let's call the ellipse function.", 'start': 476.624, 'duration': 1.581}, {'end': 485.771, 'text': 'And I think our life might be easier if I just do translate to the center.', 'start': 480.126, 'duration': 5.645}], 'summary': 'Creating a 400x400 window with a background of 0 and stroke of 255, then using the ellipse function with translation to the center.', 'duration': 29.392, 'max_score': 456.379, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q456379.jpg'}, {'end': 596.719, 'src': 'embed', 'start': 562.837, 'weight': 1, 'content': [{'end': 569.658, 'text': "I'm going to say, and let's actually, let's make a variable, a global variable called r, which is equal to 200.", 'start': 562.837, 'duration': 6.821}, {'end': 576.999, 'text': "So I'm going to say r times 2, r times 2, r times 2, r times 2.", 'start': 569.658, 'duration': 7.341}, {'end': 579.68, 'text': "I'm going to make a random number.", 'start': 576.999, 'duration': 2.681}, {'end': 590.314, 'text': 'between negative r and r, and a y, which is a random number between negative r and r.', 'start': 580.936, 'duration': 9.378}, {'end': 592.178, 'text': "Then I'm going to draw a point.", 'start': 590.314, 'duration': 1.864}, {'end': 594.517, 'text': 'at that x, y.', 'start': 593.416, 'duration': 1.101}, {'end': 595.718, 'text': "So let's do our dart throwing.", 'start': 594.517, 'duration': 1.201}, {'end': 596.719, 'text': 'Okay, look at that.', 'start': 596.018, 'duration': 0.701}], 'summary': 'Global variable r set to 200, used in calculations and dart throwing.', 'duration': 33.882, 'max_score': 562.837, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q562837.jpg'}, {'end': 650.403, 'src': 'embed', 'start': 624.187, 'weight': 2, 'content': [{'end': 630.17, 'text': 'So now what I need to figure out is I need to count the dots that are, well, I know the total dot.', 'start': 624.187, 'duration': 5.983}, {'end': 633.351, 'text': 'And actually all of the dots.', 'start': 630.21, 'duration': 3.141}, {'end': 635.853, 'text': "I don't have to test if dots are within the square,", 'start': 633.351, 'duration': 2.502}, {'end': 640.875, 'text': "because I've set this up in such a way that it basically can only create dots that are within the square.", 'start': 635.853, 'duration': 5.022}, {'end': 644.357, 'text': 'So what I need to do is determine how many dots are within the circle.', 'start': 641.255, 'duration': 3.102}, {'end': 646.419, 'text': 'So let me do this.', 'start': 645.257, 'duration': 1.162}, {'end': 650.403, 'text': "I'm going to say if r, so first I need to get the distance.", 'start': 646.439, 'duration': 3.964}], 'summary': 'Determining the number of dots within a circle based on distance calculation', 'duration': 26.216, 'max_score': 624.187, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q624187.jpg'}, {'end': 789.538, 'src': 'embed', 'start': 758.594, 'weight': 3, 'content': [{'end': 760.436, 'text': 'I could just check all of the pixels.', 'start': 758.594, 'duration': 1.842}, {'end': 762.659, 'text': 'But I like the random method.', 'start': 760.857, 'duration': 1.802}, {'end': 767.124, 'text': 'And let me make these colors quite a bit more different.', 'start': 763.56, 'duration': 3.564}, {'end': 768.765, 'text': 'There we go.', 'start': 768.405, 'duration': 0.36}, {'end': 770.327, 'text': "So we can see I've got some blue ones.", 'start': 768.785, 'duration': 1.542}, {'end': 776.052, 'text': "And you can see if they're on the line, Depending on where they are, because I have a stroke width of 2, they're either blue or green.", 'start': 770.627, 'duration': 5.425}, {'end': 777.492, 'text': 'So that could use some finesse.', 'start': 776.072, 'duration': 1.42}, {'end': 783.115, 'text': "In the chat, the live chat that's going on, I see someone's asking, what is float? Float is the data type.", 'start': 778.193, 'duration': 4.922}, {'end': 789.538, 'text': 'So, unlike in JavaScript, which a lot of my other tutorials in, I would just say let x or var x or const x,', 'start': 783.135, 'duration': 6.403}], 'summary': 'Using random method to generate different colored pixels, with room for improvement in distinguishing colors and explaining data types.', 'duration': 30.944, 'max_score': 758.594, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q758594.jpg'}], 'start': 456.379, 'title': 'Dart throwing and shape counting', 'summary': "Covers simulating dart throwing using processing's random number function and drawing/counting dots within a shape using a programming language, emphasizing randomness and visual representation.", 'chapters': [{'end': 596.719, 'start': 456.379, 'title': 'Dart throwing simulation', 'summary': "Demonstrates creating a window, drawing an ellipse and rectangle, setting stroke weight and mode, and simulating dart throwing using processing's random number function within a loop.", 'duration': 140.34, 'highlights': ['The chapter demonstrates how to create a window with a background and draw an ellipse and rectangle with specific dimensions and styles.', 'It explains the concept of translating the origin to the center, making it easier to position shapes and elements.', "It illustrates the usage of the processing's random number function to simulate dart throwing, with a global variable for radius and the generation of random coordinates within the specified range."]}, {'end': 777.492, 'start': 596.939, 'title': 'Drawing dots and counting shapes', 'summary': 'Discusses the process of drawing and counting dots within a shape using a programming language, including the use of the pythagorean theorem and the importance of randomness in the method, to create a visual representation.', 'duration': 180.553, 'highlights': ['The process involves drawing dots in a specific setup and determining the number of dots within a circle, which is achieved by using the Pythagorean theorem to calculate the distance from the center to each dot.', 'The use of randomness is highlighted as a preferred method for checking all the pixels and creating different colored dots, adding an element of visual finesse to the representation.', "The chapter showcases the author's preference for using randomness to create visual representations, despite acknowledging alternative methods such as checking all pixels for determining dot placement."]}], 'duration': 321.113, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q456379.jpg', 'highlights': ['The chapter demonstrates how to create a window with a background and draw shapes with specific dimensions and styles.', "It illustrates the usage of the processing's random number function to simulate dart throwing, with a global variable for radius and the generation of random coordinates within the specified range.", 'The process involves drawing dots in a specific setup and determining the number of dots within a circle, achieved by using the Pythagorean theorem to calculate the distance from the center to each dot.', 'The use of randomness is highlighted as a preferred method for checking all the pixels and creating different colored dots, adding an element of visual finesse to the representation.']}, {'end': 1087.518, 'segs': [{'end': 825.804, 'src': 'embed', 'start': 799.348, 'weight': 3, 'content': [{'end': 809.856, 'text': "So what I'm going to do is I'm going to say int, I'm going to use an integer, total equals 0, and int circle equals 0.", 'start': 799.348, 'duration': 10.508}, {'end': 813.518, 'text': 'So this is going to be total is going to mean the total number of dots.', 'start': 809.856, 'duration': 3.662}, {'end': 817.021, 'text': 'Circle is going to be the number of dots that are in the circle.', 'start': 814.119, 'duration': 2.902}, {'end': 825.804, 'text': "And what I'm going to do is, I am going to say now I'm going to look back at my formula right?", 'start': 818.339, 'duration': 7.465}], 'summary': 'Using integers to count dots in a circle.', 'duration': 26.456, 'max_score': 799.348, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q799348.jpg'}, {'end': 880.234, 'src': 'embed', 'start': 853.568, 'weight': 5, 'content': [{'end': 859.612, 'text': 'Float pi equals four times circle divided by total.', 'start': 853.568, 'duration': 6.044}, {'end': 861.974, 'text': "And let's put those in parentheses just for fun.", 'start': 859.892, 'duration': 2.082}, {'end': 862.794, 'text': "Now here's the thing.", 'start': 862.014, 'duration': 0.78}, {'end': 864.015, 'text': "There's a couple problems with this.", 'start': 862.974, 'duration': 1.041}, {'end': 865.356, 'text': 'Number one.', 'start': 864.635, 'duration': 0.721}, {'end': 869.43, 'text': "Total, I don't want total to be zero.", 'start': 866.769, 'duration': 2.661}, {'end': 875.052, 'text': "It will never be zero because I'm going to immediately say total plus plus.", 'start': 870.17, 'duration': 4.882}, {'end': 877.473, 'text': "As soon as I pick a point, I'm increasing.", 'start': 875.192, 'duration': 2.281}, {'end': 880.234, 'text': 'So at least the first time it runs through this, total will be one.', 'start': 877.493, 'duration': 2.741}], 'summary': 'Using the formula, pi = 4 * circle / total, ensures total is never zero, as it is incremented at least once to become one.', 'duration': 26.666, 'max_score': 853.568, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q853568.jpg'}, {'end': 934.228, 'src': 'embed', 'start': 903.724, 'weight': 4, 'content': [{'end': 912.847, 'text': "So even if I say 10 divided by 20, that's 0 remainder 10, or 20 divided by 20.", 'start': 903.724, 'duration': 9.123}, {'end': 916.551, 'text': '19 divided by 20 is 0, remainder 19.', 'start': 912.847, 'duration': 3.704}, {'end': 918.392, 'text': "So it's always going to give me the 0.", 'start': 916.551, 'duration': 1.841}, {'end': 921.215, 'text': 'So I need to explicitly convert one of these to a float.', 'start': 918.392, 'duration': 2.823}, {'end': 924.418, 'text': 'I think I might change this to double for more precision.', 'start': 921.235, 'duration': 3.183}, {'end': 934.228, 'text': 'But this should now give me, you can see here, I am slowly and slowly getting closer and closer perhaps to the value of pi.', 'start': 924.679, 'duration': 9.549}], 'summary': 'Discussing division and precision in code, aiming to approximate the value of pi.', 'duration': 30.504, 'max_score': 903.724, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q903724.jpg'}, {'end': 977.871, 'src': 'embed', 'start': 952.507, 'weight': 2, 'content': [{'end': 965.873, 'text': "Well, one guess that I have is that I haven't been so exactly thoughtful about my distance check that maybe that sort of border of what's on the line versus not on the line is something that I need to think about more deeply.", 'start': 952.507, 'duration': 13.366}, {'end': 970.707, 'text': 'The resolution is kind of an issue there.', 'start': 968.066, 'duration': 2.641}, {'end': 977.871, 'text': 'But the other issue might be just the way that floating point math works in the Java programming language.', 'start': 971.467, 'duration': 6.404}], 'summary': 'Issue with distance check and floating point math in java programming language.', 'duration': 25.364, 'max_score': 952.507, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q952507.jpg'}, {'end': 1053.898, 'src': 'embed', 'start': 998.826, 'weight': 0, 'content': [{'end': 1006.811, 'text': "So one thing I can absolutely do is, there's no reason why I couldn't just put a little for loop in here and say, hey, let's do 100 points per frame.", 'start': 998.826, 'duration': 7.985}, {'end': 1024.233, 'text': "And what I'm going to do is I'm going to say Let's make a pi a variable outside of that loop, just so when the loop finishes,", 'start': 1010.613, 'duration': 13.62}, {'end': 1025.795, 'text': 'I can take a look at what the value of pi is.', 'start': 1024.233, 'duration': 1.562}, {'end': 1027.637, 'text': 'So now I can do 100 points at a time.', 'start': 1026.015, 'duration': 1.622}, {'end': 1032.16, 'text': 'And you can see how much faster this is sort of filling up the drawing.', 'start': 1027.957, 'duration': 4.203}, {'end': 1035.983, 'text': 'And we can now go look and see what have I got here.', 'start': 1033.281, 'duration': 2.702}, {'end': 1040.207, 'text': 'Yeah, so I think we just have a lot of randomness here.', 'start': 1036.464, 'duration': 3.743}, {'end': 1041.188, 'text': "And now I'm getting 3.141.", 'start': 1040.587, 'duration': 0.601}, {'end': 1043.108, 'text': "We're converging as best we can.", 'start': 1041.188, 'duration': 1.92}, {'end': 1049.655, 'text': "I think we've done a pretty good job at approximating pi.", 'start': 1046.732, 'duration': 2.923}, {'end': 1051.036, 'text': 'I think maybe I could actually be done.', 'start': 1049.675, 'duration': 1.361}, {'end': 1053.898, 'text': 'A couple of things that people noted.', 'start': 1051.056, 'duration': 2.842}], 'summary': 'Using a for loop, 100 points per frame, approximated pi to 3.141, converged well.', 'duration': 55.072, 'max_score': 998.826, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q998826.jpg'}], 'start': 778.193, 'title': 'Calculating pi with precision', 'summary': 'Discusses calculating the value of pi using float data type, highlighting the issues with integer arithmetic and suggesting adjustments in java code to achieve more efficient and accurate approximation, resulting in a precise calculation of pi.', 'chapters': [{'end': 952.167, 'start': 778.193, 'title': 'Calculating pi using float', 'summary': 'Discusses using float data type to calculate the value of pi, highlighting the issues with integer arithmetic and the need for converting to float to achieve precision in the calculation.', 'duration': 173.974, 'highlights': ['The total and circle variables are used to count the total number of dots and the number of dots within the circle, respectively, in order to calculate the value of pi.', 'The issue with integer arithmetic is explained, demonstrating the need to convert one of the variables to a float to achieve accurate results in the calculation of pi.', 'The process of incrementing the total and circle variables to avoid division by zero and ensure accurate calculation of pi is described.']}, {'end': 1087.518, 'start': 952.507, 'title': 'Approximating pi with java', 'summary': 'Discusses the issues with precision and performance in approximating pi using java, suggesting adjustments to the code, including increasing point generation and avoiding square root calculations, resulting in a more efficient and accurate approximation of pi.', 'duration': 135.011, 'highlights': ['The chapter discusses the issues with precision and performance in approximating pi using Java, suggesting adjustments to the code. The speaker identifies the need for more precision in the data type and the resolution issue, highlighting the potential impact of floating point math in the Java programming language.', 'Increasing point generation and avoiding square root calculations result in a more efficient and accurate approximation of pi. The speaker implements a for loop to generate 100 points per frame, improving the speed of drawing and converging towards the approximation of pi, while also considering removing the square root calculation for better performance.', 'The speaker concludes the chapter with a successful approximation of pi and acknowledges potential optimizations. The speaker achieves a successful approximation of pi, reaching the value of 3.141 and notes potential optimizations such as removing the square root calculation and experimenting with larger numbers of points for further accuracy.']}], 'duration': 309.325, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q778193.jpg', 'highlights': ['The speaker concludes the chapter with a successful approximation of pi, reaching the value of 3.141 and notes potential optimizations such as removing the square root calculation and experimenting with larger numbers of points for further accuracy.', 'Increasing point generation and avoiding square root calculations result in a more efficient and accurate approximation of pi. The speaker implements a for loop to generate 100 points per frame, improving the speed of drawing and converging towards the approximation of pi, while also considering removing the square root calculation for better performance.', 'The chapter discusses the issues with precision and performance in approximating pi using Java, suggesting adjustments to the code. The speaker identifies the need for more precision in the data type and the resolution issue, highlighting the potential impact of floating point math in the Java programming language.', 'The total and circle variables are used to count the total number of dots and the number of dots within the circle, respectively, in order to calculate the value of pi.', 'The issue with integer arithmetic is explained, demonstrating the need to convert one of the variables to a float to achieve accurate results in the calculation of pi.', 'The process of incrementing the total and circle variables to avoid division by zero and ensure accurate calculation of pi is described.']}, {'end': 1305.385, 'segs': [{'end': 1136.886, 'src': 'embed', 'start': 1112.308, 'weight': 0, 'content': [{'end': 1118.032, 'text': "And so floating point numbers, there's an infinite amount of decimal numbers between any two integers.", 'start': 1112.308, 'duration': 5.724}, {'end': 1121.135, 'text': "But we don't have an infinite amount of memory on our computer.", 'start': 1118.473, 'duration': 2.662}, {'end': 1123.236, 'text': 'So we allocate a certain number of bits.', 'start': 1121.195, 'duration': 2.041}, {'end': 1125.918, 'text': 'So floating points allocate a certain number of bits.', 'start': 1123.637, 'duration': 2.281}, {'end': 1127.82, 'text': 'Doubles allocate more.', 'start': 1126.299, 'duration': 1.521}, {'end': 1134.345, 'text': "So if we really need to do precise mathematics, and then there's other Java classes and implementations for really big numbers.", 'start': 1128.02, 'duration': 6.325}, {'end': 1136.886, 'text': "But let's at least change this to double.", 'start': 1134.405, 'duration': 2.481}], 'summary': 'Floating point numbers use finite memory, with doubles allocating more bits for precise mathematics.', 'duration': 24.578, 'max_score': 1112.308, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1112308.jpg'}, {'end': 1175.716, 'src': 'embed', 'start': 1153.301, 'weight': 1, 'content': [{'end': 1161.109, 'text': "I don't think I need to change all of these, but now I should see that this, and by the way, I don't need to calculate it.", 'start': 1153.301, 'duration': 7.808}, {'end': 1162.15, 'text': "I don't know why I did that.", 'start': 1161.129, 'duration': 1.021}, {'end': 1164.911, 'text': 'I can just calculate it once there.', 'start': 1163.05, 'duration': 1.861}, {'end': 1165.912, 'text': 'And I wrote float.', 'start': 1164.951, 'duration': 0.961}, {'end': 1167.152, 'text': "And let's make this double.", 'start': 1166.292, 'duration': 0.86}, {'end': 1168.513, 'text': "OK, so now let's take a look at this.", 'start': 1167.272, 'duration': 1.241}, {'end': 1175.716, 'text': 'And one thing we can see is already there are more digits appearing in the print line statement.', 'start': 1169.273, 'duration': 6.443}], 'summary': 'Changing data types to improve precision and avoid unnecessary calculations.', 'duration': 22.415, 'max_score': 1153.301, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1153301.jpg'}, {'end': 1307.767, 'src': 'embed', 'start': 1281.31, 'weight': 2, 'content': [{'end': 1287.115, 'text': "And it seems to be running at a perfectly reasonable frame rate, so I'm actually going to try to do this 10, 000 times per frame.", 'start': 1281.31, 'duration': 5.805}, {'end': 1290.917, 'text': "Now it's a little bit slow.", 'start': 1289.777, 'duration': 1.14}, {'end': 1294.12, 'text': 'So I want my animation to be fast.', 'start': 1291.938, 'duration': 2.182}, {'end': 1298.7, 'text': 'Oh, that was 100, 000.', 'start': 1294.58, 'duration': 4.12}, {'end': 1299.741, 'text': "Let's just go with 10, 000.", 'start': 1298.7, 'duration': 1.041}, {'end': 1301.282, 'text': "OK So let's take a look.", 'start': 1299.741, 'duration': 1.541}, {'end': 1302.483, 'text': "OK, I'll be back in a minute.", 'start': 1301.342, 'duration': 1.141}, {'end': 1305.385, 'text': "Let's see how many digits we can kind of get and see how close we're doing.", 'start': 1302.563, 'duration': 2.822}, {'end': 1307.767, 'text': "Hey, I'm back again.", 'start': 1306.867, 'duration': 0.9}], 'summary': 'Testing animation speed at 10,000 frames per second.', 'duration': 26.457, 'max_score': 1281.31, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1281310.jpg'}], 'start': 1088.039, 'title': 'Using double data type in java', 'summary': 'Explores the usage of double data type in java for precise mathematics, discussing the implications of using double over float and the impact on the precision of calculations. it also includes a program to demonstrate the effect of using double data type on the output.', 'chapters': [{'end': 1305.385, 'start': 1088.039, 'title': 'Using double data type in java', 'summary': 'Explores the usage of double data type in java for precise mathematics, discussing the implications of using double over float and the impact on the precision of calculations, while running a program to demonstrate the effect of using double data type on the output.', 'duration': 217.346, 'highlights': ['Double data type allocation for precise mathematics The chapter discusses the need for precise mathematics and the allocation of bits for double data type, emphasizing its capability to handle a larger range of numbers and demonstrating the impact on the precision of calculations.', 'Effect of using double data type on output precision The program is run to demonstrate the impact of using double data type on the precision of calculations, as evident from the increased number of digits appearing in the print line statement and the consistent output of 1.41, showcasing the improved precision.', "Optimizing animation performance by adjusting frame rate The chapter explores optimizing animation performance by adjusting the frame rate, aiming for a faster animation by running the program 10,000 times per frame, while evaluating the impact on the program's speed and precision."]}], 'duration': 217.346, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1088039.jpg', 'highlights': ['Double data type allocation for precise mathematics The chapter discusses the need for precise mathematics and the allocation of bits for double data type, emphasizing its capability to handle a larger range of numbers and demonstrating the impact on the precision of calculations.', 'Effect of using double data type on output precision The program is run to demonstrate the impact of using double data type on the precision of calculations, as evident from the increased number of digits appearing in the print line statement and the consistent output of 1.41, showcasing the improved precision.', "Optimizing animation performance by adjusting frame rate The chapter explores optimizing animation performance by adjusting the frame rate, aiming for a faster animation by running the program 10,000 times per frame, while evaluating the impact on the program's speed and precision."]}, {'end': 1641.023, 'segs': [{'end': 1361.344, 'src': 'embed', 'start': 1331.895, 'weight': 0, 'content': [{'end': 1340.877, 'text': 'So processing natively has the constant pi, but Java also has the constant pi that is in the math package.', 'start': 1331.895, 'duration': 8.982}, {'end': 1342.837, 'text': 'So let me look at both of those.', 'start': 1341.797, 'duration': 1.04}, {'end': 1344.938, 'text': 'And you can see that that one is a double.', 'start': 1343.057, 'duration': 1.881}, {'end': 1347.638, 'text': "So this is actually what's stored.", 'start': 1345.418, 'duration': 2.22}, {'end': 1351.859, 'text': "It's not that many digits in math.pi in Java.", 'start': 1347.678, 'duration': 4.181}, {'end': 1361.344, 'text': "So what I'm going to do is I am going to create, I'm going to create a variable called recordPy.", 'start': 1352.279, 'duration': 9.065}], 'summary': 'Comparing the constant pi in processing and java, stored as a double in java.', 'duration': 29.449, 'max_score': 1331.895, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1331895.jpg'}, {'end': 1465.481, 'src': 'embed', 'start': 1396.848, 'weight': 1, 'content': [{'end': 1401.852, 'text': "So I'm going to take the difference between math.py and the record.py.", 'start': 1396.848, 'duration': 5.004}, {'end': 1406.214, 'text': 'then. so this is actually really the record difference.', 'start': 1401.852, 'duration': 4.362}, {'end': 1417.687, 'text': "then I'm going to look at the difference between the pi I just calculated, math.pi minus the pi I just calculated.", 'start': 1406.214, 'duration': 11.473}, {'end': 1430.619, 'text': "So if the difference is less than the record difference, if we've gotten one that's closer, then the difference is now.", 'start': 1418.107, 'duration': 12.512}, {'end': 1439.845, 'text': 'oh, the record difference is now the difference and the record pi.', 'start': 1430.619, 'duration': 9.226}, {'end': 1441.245, 'text': 'why did I use an underscore??', 'start': 1439.845, 'duration': 1.4}, {'end': 1442.306, 'text': 'Did I use an underscore??', 'start': 1441.285, 'duration': 1.021}, {'end': 1444.226, 'text': "That's sort of unnecessary.", 'start': 1443.146, 'duration': 1.08}, {'end': 1453.769, 'text': 'Record pi equals zero, and then record pi, then record pi is that new pi.', 'start': 1444.526, 'duration': 9.243}, {'end': 1462.398, 'text': 'And what I could do is whenever I have a new record, I could print out Record pi.', 'start': 1454.989, 'duration': 7.409}, {'end': 1465.481, 'text': "So let's take a look and see what I get in the console there.", 'start': 1462.638, 'duration': 2.843}], 'summary': 'Analyzing differences in math.py and record.py, updating record pi when a closer value is found.', 'duration': 68.633, 'max_score': 1396.848, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1396848.jpg'}, {'end': 1529.644, 'src': 'heatmap', 'start': 1488.228, 'weight': 3, 'content': [{'end': 1491.53, 'text': 'This is now currently the record.', 'start': 1488.228, 'duration': 3.302}, {'end': 1497.093, 'text': "1.415926 Hey, I don't know.", 'start': 1491.55, 'duration': 5.543}, {'end': 1503.036, 'text': "How many digits have I gotten correct? All right, so let's go look at the actual digits of pi.", 'start': 1497.593, 'duration': 5.443}, {'end': 1508.199, 'text': "So I'm going to go to pi-day.org slash million.", 'start': 1504.037, 'duration': 4.162}, {'end': 1511.421, 'text': "And I don't need that many of them.", 'start': 1509.94, 'duration': 1.481}, {'end': 1516.656, 'text': 'This is going to be plenty, just the first line here.', 'start': 1514.195, 'duration': 2.461}, {'end': 1519.358, 'text': "Let's open up TextEdit.", 'start': 1517.497, 'duration': 1.861}, {'end': 1521.359, 'text': "Let's put this in here.", 'start': 1520.299, 'duration': 1.06}, {'end': 1526.442, 'text': "And let's make this a little bit bigger.", 'start': 1523.52, 'duration': 2.922}, {'end': 1529.644, 'text': "Let's go back to the processing sketch.", 'start': 1528.143, 'duration': 1.501}], 'summary': 'Record set at 1.415926 digits of pi.', 'duration': 32.051, 'max_score': 1488.228, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1488228.jpg'}, {'end': 1638.661, 'src': 'embed', 'start': 1597.75, 'weight': 4, 'content': [{'end': 1598.37, 'text': "There's so many.", 'start': 1597.75, 'duration': 0.62}, {'end': 1600.792, 'text': "You could think about how you're drawing this.", 'start': 1598.57, 'duration': 2.222}, {'end': 1604.495, 'text': "You could make the random numbers double that you're picking.", 'start': 1601.032, 'duration': 3.463}, {'end': 1605.475, 'text': "I don't know if that would really help.", 'start': 1604.515, 'duration': 0.96}, {'end': 1610.139, 'text': 'You could use my favorite website, random.org, which has an API for random numbers.', 'start': 1605.736, 'duration': 4.403}, {'end': 1612.341, 'text': "It's really not going to make your program run faster.", 'start': 1610.159, 'duration': 2.182}, {'end': 1616.044, 'text': 'But there is so much that you could try to do.', 'start': 1612.681, 'duration': 3.363}, {'end': 1624.91, 'text': 'So if you make something with this coding challenge, please share it with me in the comments below.', 'start': 1619.186, 'duration': 5.724}, {'end': 1627.572, 'text': 'You can also go to thecodingtrain.com website.', 'start': 1624.95, 'duration': 2.622}, {'end': 1629.894, 'text': "There's a place where you can link to your shared version.", 'start': 1627.593, 'duration': 2.301}, {'end': 1633.977, 'text': 'I will also release a JavaScript version of this that you can run in the browser.', 'start': 1629.994, 'duration': 3.983}, {'end': 1637.56, 'text': 'And maybe actually that might be an easier way to also display the results.', 'start': 1634.138, 'duration': 3.422}, {'end': 1638.661, 'text': 'So thanks for watching.', 'start': 1637.6, 'duration': 1.061}], 'summary': 'Experiment with doubling random numbers, using random.org api, and sharing results for coding challenge.', 'duration': 40.911, 'max_score': 1597.75, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1597750.jpg'}], 'start': 1306.867, 'title': 'Tracking and comparing constants in java', 'summary': 'Delves into tracking and comparing the constant pi in java, optimizing a program by updating and printing the record pi value, and involves a coding challenge to compare the digits of pi to a generated sequence, aiming for accuracy, with a suggestion for potential improvements and a call for viewer participation.', 'chapters': [{'end': 1497.093, 'start': 1306.867, 'title': 'Tracking and comparing constants in java', 'summary': 'Discusses the process of tracking and comparing constant pi in java, and optimizing a program by continuously updating and printing the record pi value.', 'duration': 190.226, 'highlights': ['The program aims to continuously update and print the record pi value, utilizing the constant pi in Java and the math package.', 'A variable called recordPy is created and initialized to zero to store the record difference between math.pi and the calculated pi.', 'The program calculates the difference between math.pi and the record.pi, updates the record difference if a closer value is found, and prints the record pi value in the console.']}, {'end': 1641.023, 'start': 1497.593, 'title': 'Comparing digits of pi', 'summary': 'Involves a coding challenge where the speaker compares the digits of pi to a generated sequence, aiming for accuracy, with a suggestion for potential improvements and a call for viewer participation.', 'duration': 143.43, 'highlights': ['The speaker compares the digits of pi to a generated sequence to evaluate accuracy, identifying correct digits and making adjustments to improve accuracy.', 'The speaker suggests potential improvements such as plotting the difference, visualizing the numbers, and using the random.org API for generating numbers.', 'The speaker encourages viewer participation and sharing of their versions of the coding challenge, with plans to release a JavaScript version for easier display of results.']}], 'duration': 334.156, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/5cNnf_7e92Q/pics/5cNnf_7e92Q1306867.jpg', 'highlights': ['The program continuously updates and prints the record pi value in Java.', 'A variable called recordPy is created and initialized to zero to store the record difference between math.pi and the calculated pi.', 'The program calculates the difference between math.pi and the record.pi, updates the record difference if a closer value is found, and prints the record pi value in the console.', 'The speaker compares the digits of pi to a generated sequence to evaluate accuracy, identifying correct digits and making adjustments to improve accuracy.', 'The speaker suggests potential improvements such as plotting the difference, visualizing the numbers, and using the random.org API for generating numbers.', 'The speaker encourages viewer participation and sharing of their versions of the coding challenge, with plans to release a JavaScript version for easier display of results.']}], 'highlights': ['The speaker concludes the chapter with a successful approximation of pi, reaching the value of 3.141 and notes potential optimizations such as removing the square root calculation and experimenting with larger numbers of points for further accuracy.', 'The ratio of the area of a circle to the area of a square can be expressed as a ratio, pi r squared to 4r squared, with the ratio simplifying to pi divided by 4.', 'The process involves drawing dots in a specific setup and determining the number of dots within a circle, achieved by using the Pythagorean theorem to calculate the distance from the center to each dot.', 'The program continuously updates and prints the record pi value in Java.', 'The chapter discusses the need for precise mathematics and the allocation of bits for double data type, emphasizing its capability to handle a larger range of numbers and demonstrating the impact on the precision of calculations.']}