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Technology & Mathematics

Dive into the fascinating world where technology meets mathematics through video games. This exploration covers simple classifications, height and width pictorial explanations, and modeling techniques that illuminate how creatures interact with their environments. Delve into concepts like hit detection in 3D games and the principles of projectile motion using quadratics to simulate jumping mechanics. Additionally, the discussion includes efficient search methods, comparing linear and binary searches, by analyzing worst-case scenarios in phonebook searches.

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Technology & Mathematics

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  1. Technology & Mathematics Michael Herzog Qiyam Tung

  2. Logicomix

  3. Simple Classification Height Width Pictorial Explanation What creatures fall between the lines?

  4. Modeling Videogames and Mathematics 3D Games and Hit Detection

  5. Video Games and Mathematics Pictorial Explanation Banjo “switches gears” once he touches the surface of the water.

  6. Video Games and Mathematics (0.5,6) (1,5) (2,1) • y1=2x1+3, y1 = 6 • 6=2(0.5)+3 = 4 • False! • 5=2(1)+3 = 5 • True! • 1=2(2)+3 =7 • False!

  7. Projectile Motion

  8. Simulating Jumping with Quadratics Task: decide which model is better for simulating a jump and find their coefficients.

  9. Simulating Jumping with Quadratics The actual code for the two models

  10. Programming Synthetic Division

  11. Algorithm Analysis • How long would it take to find any name in a phonebook in the worst case scenario?

  12. Search Time 1 2 3 4 height =log2 (n) 2 (base) = number of children per node height = seconds it will take to search n = the number of names.

  13. Comparing Linear and Binary Searches y = time x = number of names

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