Nina del Ser - Mathematics
Contents
Introduction 108
Solving the original problem 109
The ellipse 110
Changing the angular speeds of the rotors 114
Loops, spikes, or smooth curvatures? 119
Convexity 121
Extra arms for the Octopus
123
Conclusion 126
Bibliography 126
Abstract
This essay takes a relatvely simple original problem-which involves
working out the mechanics and mapping the motion of a funfair ride
known as the “Octopus”-and then tries to expand on it by changing
parameters such as the speeds, lengths and even the number of rotors
which compose it. Experimenting with these parameters produces an
infinite range of curves, which are not only beautiful to look at, but
were also very helpful in formulating several sets of “rules” for how any
“Octopus”- generated curve should look (for instance, how many axes
of symmetry it should have), given its basic parameters (rotor length and
speed).
A range of conclusions were reached; for instance: given that the speed
of the primary rotor is 1 rad/s, it is the highest common factor of all the
rotor speeds, irrespective of the number of rotors, which defines the
rotational symmetry of the curve generated. Another conclusion involves
the velocity and acceleration vectors and their role in defining whether an
Octopus curve will have loops, spikes, and concave or convex lines. Thus,
even curves that look completely random are actually following a very
strict set of rules and patterns, which we can understand.
107