Math in Basketball Group number 9-17 Our Team Picture taken from:

Our Team Zhang Shukai 3S2(24) Mao Ziming 3S2(17) Cheng Dongyan 3S2(1) Picture taken form:

Objectives Research problems Introduction We: Basketball Fans Others: 2-D Others: Air resistance and rotation We: 3-D, possibility ● 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 angle and height of scoring on every points on the court.

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 height of scoring on every points on the court?

TerminologyField of Math Bank shot A shot that hits the backboard before hitting the rim or going through the net. Free throw line A restricted area on the court which allow unopposed attempts to score points. Swish A shot which goes through the net without hitting the backboard or rim. Brick A shot that hits the rim. Wiggle room. The area on the backboard where ball can go through the net if it hits. Section of incidence The intersection of the basket in three- dimensional space with the plane which is perpendicular to the direction of movement of the basketball Objectives Introduction Research problems

Field of Math ●Solid geometry ●Calculus ●Algebra Terminology Research problems

Experimenta l approach Plane geometry approach Function approach Literature Review Literature Review

Experimental approach Silverberg (2012) made use of multiple 3-D simulations of basketball trajectories to determine the optimum release conditions for the free throw in men's basketball Picture taken from:

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:

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

Picture taken from: Baseline 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 PLANE GEOMETRY APPROACH

Picture taken from: “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 PLANE GEOMETRY APPROACH

Picture taken from: Duan (2009) noticed that the basket is actually not round because of the different positions of viewing. Intersection in 3-D space Perpendicular to the direction of moving of the basketball PLANE GEOMETRY APPROACH

Replace x and y by the coordinates of the points on the basket Get the function between velocity and angle. Function approach picture taken from : FattachType%3DPDF%26id%3D31255&hl=zh- CN&sa=T&oi=ggp&ct=res&cd=5&ei=lz3QVOm7MceEqgGQ9YHYCA&scisig=AAGBfm3XcoVU6si- tVR5aBJXA1fUTY9inA&nossl=1&ws=1366x673

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. METHODOLOGY

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

By end of February Completion of research proposal. The whole March Finish the special point’s calculation: swish on every points, bank shot on certain points. March to early April Prepare for the Prelim Judging. 6 AprilPreliminary Round. Early April to July Calculate function of trajectory of bank shot on every points (From special to general case). Build up model in three dimension. June HolidayCalculate function of probability of shooting points on the field. Time line

Late June to early July Prepare the presentation. 9 JulySemi Final Round. Mid-July to late July Calculate what is the best angle and height to shoot, which part of the board is easier to let ball rebounds to basket. Summary the conditions. Reflect, extend and apply the mathematics model in other parts. Late July to early August Prepare presentation, slides and write the report. 23 AugFinal Round Time line

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 Silverberg, L.M. (2012). & Wagner, K. (2012). Science Has Calculated the Perfect Basketball Shot Retrieved on 14 Feb 2015 from basketball-shot Gorski, C. (2011). Best “sweet spots” on the backboard Retrieved on 24 Feb 2015 from Brabandere, S.D. (2014). Basketball: The Geometry of Banking a Basket Retrieved 12 February, 2015 from projects/project_ideas/Sports_p064.shtml#procedure

Begley, S. (2011). “Nothing but net?” Basketball science has more answers Retrieved on 24 Feb 2015 from idUSBRE86K0BG Yan, S.S. (2008). Interesting physics in ball games Physics 37 volume year 2008 number 7 Retrieved on 1 Feb 2015 from 2Farticle%2FdownloadArticleFile.do%3FattachType%3DPDF%26id%3D31255&hl=zh- CN&sa=T&oi=ggp&ct=res&cd=5&ei=lz3QVOm7MceEqgGQ9YHYCA&scisig=AAGBfm3Xc oVU6si-tVR5aBJXA1fUTY9inA&nossl=1&ws=1366x673 reference

Thank you For your attention