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Calculus on a basketball

Project Goals In this project, we will work simultaneously on several fundamental mathematical concepts: the parameterization of the sphere, longitude and latitude, the tangent vector to a parametric curve, and rotations in space.

Parametrització bàsica de l'esfera

What are the value ranges for longitude (u) and latitude (v)?

What value ranges should longitude and latitude take if we only want to draw the northern hemisphere? And what if we want to draw only a vertical hemisphere?

In the following applet, define a point P and modify the parameterization of the sphere so that it is centered at P

In the next applet, create 6 copies of the sphere’s parameterization and adjust the longitude and latitude ranges in each copy to draw a basketball painted in 6 different colors.

In the next applet, rotate each of the six sections of the sphere around the given axis. Use the command: Rotate(object, angle, axis)



Modify the following applet so that the basketball moves along the given helix.

DEURES PER A CASA

Combine everything you’ve learned so far to make the basketball move along the helix while simultaneously rotating around the tangent line to the helix at each point.