South Pointing Chariot

This chariot was first made by a Chinese king who asked his men to build a chariot which always points in the direction of his kingdom, no matter where the chariot went.
And it doesn’t use any compass but differential gears to keep the man in the same direction. It was the first use of differential gears in the world.

Spherical Tetrahedron

The interior angles of these triangles do not add to 180 degrees (like planar triangles). The tetrahedron is formed by joining 6 great circles (circles whose radius is equal to the radius of the sphere).

Triangular Wave car

This car draws triangular wave when it moves!

Triangular wave means that the y-component is proportional to the x-component  (which is the distance traveled by the car).

The y-component is the half circumference of the middle gear and the x-component is the circumference of the car wheel. In our case, both the radii are same.

Thus, the distance traveled in y-direction is half of that in x-direction.

Therefore, the slope of the lines, tan θ = 1/2