Abstract:
The “Boat Problem” is the Calculus problem that initially got John interested in Math, which led to an Electrical Engineering degree from Penn State and ultimately to a job at Microsoft working at XBox.
John believes he can leverage the Boat Problem against the prospects of a career in the Game Development arena to motivate students to become more interested in Math.
The Boat Problem
Jesus is fishing in a Boat on the Sea of Galilee, 5 Miles from the shore, and 12 Miles from the Apostle’s Camp. Jesus can walk on water 3 Miles per Hour, and can run on the beach 5 Miles per Hour. Where does Jesus land so that he is back at the Camp the soonest?
3 Cases
There are 3 cases that can be looked at with increasing mathematical skills necessary to solve them, using 6th grade (Ratios), 8th grade (Algebra), and 12th grade (Calculus) math.
The first case is Jesus walking straight to the shore, then running the entire 12 miles down the beach. This uses Ratios and would be at the 6th grade level. Incidentally, this would make the student better than the best Roman Mathematicians at the time of Jesus. The fact that the Roman Numeral system lacks a zero makes higher mathematics impossible.
The second case would entail Jesus walking the entire length on the water and straight to the Apostle’s camp. This uses Algebra and the Pythagorean Theorem which would be at about 8th or 9th grade level.
The third case has Jesus landing somewhere along the beach so as to minimize his travel time. This uses Calculus, and if you are good at math you can learn this in the 12th grade.
Proposal:
To illustrate the connection between the math and game development to students, a simple 2 dimensional computer game will be developed to demonstrate the 3 cases. Animation will show movement along each case’s path. The animation will have a timer and the application will have the ability to start and stop the animation.
Requirements:
Create a 2-Dimensional Game interface for the PC to demonstrate the 3 cases of the Boat Problem.
Animation with 3 images of Jesus, one for each case, moving along it’s defined path.
Ability to Show/Hide each case.
Ability to Start/Stop animation.
Timer displaying elapsed time.
Help popup screens with descriptions of the math.
