Math in Basketball Group number 9-17

Our Team

Picture taken from: www.downwithdesign.com

Our Team

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

Objectives Research problems

Introduction

We: Basketball Fans

Others: 2-D

Others: Air resistance and rotationWe: 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?

Terminology

Field 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

ObjectivesIntroduction Research problems

Field of Math

●Solid

geometry

●Calculus

●Algebra

Terminology

Research problems

Experimental approach

Plane geometry approach

Functionapproach

Literature Review

Experimental approachSilverberg (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: http://gizmodo.com/5928074/science-has-calculated-the-perfect-basketball-shot)

One thing to noteall 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

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: http://www.sciencebuddies.org/science-fair-projects/project_ideas/Sports_p064.shtml#procedure

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: http://www.sciencebuddies.org/science-fairprojects/project_ideas/Sports_p064.shtml#procedure

“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: http://chs.mesa.k12.co.us/departments/math/JohnSidanycz/documents/BasketballisMath.pptx

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 :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

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 April Preliminary 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

Holiday

Calculate function of probability of shooting

points on the field.

Time line

Late June to

early July

Prepare the presentation.

9 July Semi 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 Aug Final 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

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

• 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 fromhttp://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=AAGBfm3Xc

oVU6si-tVR5aBJXA1fUTY9inA&nossl=1&ws=1366x673

reference

Thank you

For your attentio

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