and took the gears and the gearbox apart turning them into a pile of scraps each bearing a few teeth that sparked a new idea that the teeth are important not the gear wheel so maybe they thought you could build a gear strip. to create motion you could thrust a tooth up from below into the groove one after the other. stays in motion with a larger number of teeth doing the work. but you want it to rotate rather than move in a linear fashion. so that means bending it into a circle. now it looks like this but there's a problem the teeth no longer fit neatly into the grooves a moment ago they were all triangles which fit each other perfectly so the teeth have to be curved and not just into any old curve but a logarithmic spiral. it's