An Analysis of Graphical Representations of Bowling Allison Nelson (gurly130@yahoo.com) West Davidson High School, Lexington, NC Summer Ventures in Science and Mathematics Visual and Image Processing Dr. Rahman Tashakkori, Mr. Jere Miles Appalachian State University, NC July 28, 2007

Introduction Objective: Methodology: To analyze paths of bowling balls To model the balls’ paths Methodology: Utilization of ImageJ, Windows Movie Maker, Microsoft Office Excel, MATLAB, Microsoft Paint, and http://ourworld.compuserve.com/ homepages/kennmelvin. Video clips were broken down into frames and analyzed.

The History of Bowling About 3200 BC: Artifacts in boy’s tomb Different Countries, Different Names Italy: “Bocce Ball” England: “Lawn Bowling” Nine Pins  Ten Pins Gamblers Made illegal Added one pin Modern Bowling End of 19th century 1936: Automatic Pinsetter: Gottfried Schmidt TV Bowling: 1950’s

The Clips Video clips of bowling were obtained from http://ourworld.compuserve.com/homepages/kennmelvin

Programs Used Windows Movie Maker Image J MATLAB Separate videos into image frames Image J Delete everything but center pixel of the ball Invert the image MATLAB Write a script to locate the center pixel Microsoft Office Excel Graph data and find the mathematical model

Results-Strike Ball y = -0.0212x2 + 7.102x - 332.58 R2 = 0.993 The ball followed a smooth second-order polynomial curved path. The equation above suggests that when the ball was released, the bowler intentionally put a spin on the ball to achieve the “hook” effect.

Results-Split Ball The initial coefficients of the equation indicated that the ball was initially thrown with just a bit of spin, but this spin caused it to deflect off the pins on impact. y = -0.0061x2 + 1.9434x + 48.98 R2 = 0.9274

Conclusions and Future Plans The bowling ball must be thrown a precise way to achieve a strike. Deviation=bad Both balls hooked, strike ball hooked more Need hook to strike consistently Future Plans Study speed of Balls Investigate initial angle Analyze more videos Different scenarios (spares)

Acknowledgements I would like to thank the following people: Dr. Tashakkori for giving me ideas and input, and writing the script I used in MATLAB Mr. Miles for giving me pointers on the art of research writing Ryan Belt for helping me with the technical stuff…  Ben Bucior, Ryan Belt and Kyle Rhash for (trying) to write a macro for ImageJ for me. Thanks for helping! My parents for coming to listen to me