Group number 9-17

1. Math in Basketball Our Team Group number 9-17 Picture taken from: www.downwithdesign.com

2. Our Team Cheng Dongyan 3S2(1) Mao Ziming 3S2(17) Zhang Shukai 3S2(24) Picture taken form: http://satorifrenzy.deviantart.com/art/MIB3-wallpaper-by-satorikun-302439924

3. Research problems Introduction Objectives ● To calculate the function of making bank shot and making swish on every points on the court. ● To calculate the highest possibility of scoring on every points on the court. ● To determine the optimum angleand height of scoring on every points on the court. We: Basketball Fans Others: Air resistance and rotation We: 3-D, possibility Others: 2-D

4. Research problems Introduction Objectives  ● What is the path of a swish and bank shot on every points on the court? ● What is the position on the court which has the highest possibility to shoot on target? ● What is the best angle and heightof scoring on every points on the court?

5. Research problems Introduction Objectives Field of Math Terminology

6. Research problems Field of Math Terminology • Solid geometry • Calculus • Algebra

7. Function approach Plane geometry approach Experimental approach Literature Review

8. Experimental approach Silverberg (2012) made use of multiple 3-Dsimulationsof basketball trajectories to determine the optimum release conditions for the free throw in men's basketball Picture taken from: http://gizmodo.com/5928074/science-has-calculated-the-perfect-basketball-shot)

9. One thing to note all the aim points will produce a pattern that looks like the letter “V” It shows… part of the board is more likely to make the basketball rebound into the basket. picture taken from: http://phys.org/news/2011-03-sweet-backboard.html

10. However… Silverberg’s (2012) research only focused on specificpoints on the courts and thus it could be further extended to general points on the courts. It requires many equipment to carry on the research which is not available to students.

11. PLANE GEOMETRY APPROACH • Brabandere(2014) defined the 90° position as the baseline. • Calculate the possibility of the other shot with respect to the 90° position • Easier to compare the possibility in the other positions Baseline Picture taken from: http://www.sciencebuddies.org/science-fair-projects/project_ideas/Sports_p064.shtml#procedure

12. PLANE GEOMETRY APPROACH • “Wiggle room” • Can be a good method to study the possibility of score • Only • in 2-D condition • Not considering the “back and forward” aspect Picture taken from: http://www.sciencebuddies.org/science-fairprojects/project_ideas/Sports_p064.shtml#procedure

13. PLANE GEOMETRY APPROACH • Duan (2009)noticed that the basket isactually not round because of the different positions of viewing. • Intersection in 3-D space • Perpendicular to the direction of moving of the basketball Picture taken from: http://chs.mesa.k12.co.us/departments/math/JohnSidanycz/documents/BasketballisMath.pptx

14. Function approach • Replace x and y by the coordinates of the points on the basket • Get the function between velocity and angle. picture taken from :http://scholar.google.com.sg/scholar_url?url=http%3A%2F%2Fwww.wuli.ac.cn%2FN%2Farticle%2FdownloadArticleFile.do%3FattachType%3DPDF%26id%3D31255&hl=zh-CN&sa=T&oi=ggp&ct=res&cd=5&ei=lz3QVOm7MceEqgGQ9YHYCA&scisig=AAGBfm3XcoVU6si-tVR5aBJXA1fUTY9inA&nossl=1&ws=1366x673

15. METHODOLOGY Deduce the function and graph with respect to the launch angle and the velocity, through studying swish and bank shot on the 90° position on the free throw line.

16. METHODOLOGY Calculate the angle and speed at which the percentage of shooting on target is maximum.

17. METHODOLOGY Evaluate the size of Wiggle room at different positions. Research on the relationship between the height of the basketball at the moment of release and the percentage of shooting on target.

18. Time line

19. Time line

20. reference • Duan, R. (2009). The physical model of basketball shooting motion track and hitting rate Science and Technology Consulting Herald Year 2009 number 20 Retrieved on 2 Feb 2015 from http://wenku.baidu.com/view/1812a541336c1eb91a375d61.html • Silverberg, L.M. (2012). & Wagner, K. (2012). Science Has Calculated the Perfect Basketball Shot Retrieved on 14 Feb 2015 from http://gizmodo.com/5928074/science-has-calculated-the-perfect- basketball-shot • Gorski, C. (2011). Best “sweet spots” on the backboard Retrieved on 24 Feb 2015 from http://phys.org/news/2011-03-sweet-backboard.html • Brabandere, S.D. (2014). Basketball: The Geometry of Banking a Basket Retrieved 12 February, 2015 from http://www.sciencebuddies.org/science-fair- projects/project_ideas/Sports_p064.shtml#procedure

21. http://scholar.google.com.sg/scholar_url?url=http%3A%2F%2Fwww.wuli.ac.cn%2FN%2Farticle%2FdownloadArticleFile.do%3FattachType%3DPDF%26id%3D31255&hl=zh-CN&sa=T&oi=ggp&ct=res&cd=5&ei=lz3QVOm7MceEqgGQ9YHYCA&scisig=AAGBfm3XcoVU6si-tVR5aBJXA1fUTY9inA&nossl=1&ws=1366x673http://scholar.google.com.sg/scholar_url?url=http%3A%2F%2Fwww.wuli.ac.cn%2FN%2Farticle%2FdownloadArticleFile.do%3FattachType%3DPDF%26id%3D31255&hl=zh-CN&sa=T&oi=ggp&ct=res&cd=5&ei=lz3QVOm7MceEqgGQ9YHYCA&scisig=AAGBfm3XcoVU6si-tVR5aBJXA1fUTY9inA&nossl=1&ws=1366x673 reference • Begley, S. (2011). “Nothing but net?” Basketball science has more answers Retrieved on 24 Feb 2015 from http://www.reuters.com/article/2012/07/21/us-oly-science-bask-adv- idUSBRE86K0BG20120721 • Yan, S.S. (2008). Interesting physics in ball games Physics 37 volume year 2008 number 7 Retrieved on 1 Feb 2015 from

22. Thank you For your attention