On the equitable distribution of points on the circle

TL;DRAbstract

In this thesis, we discuss the problem of breaking a stick representing resources, so that, as recipients arrive one at a time they get approximately even parts. To do this, we model the placement of points evenly distributed on the circle.\nThe thesis is in two parts, firstly a review of the various models including the Stick Breaking model of Erdos, hopping around the circle based on the Steinhaus three gap theorem (with Golden (Fibonacci) hops being optimal), a Binary Splitting model and Random distributions.\nThe second part consists of comparing and contrasting these models using various measures, such as, largest and smallest gap and overall discrepancies.\nThe second part consists of comparing and contrasting these models using various measures, such as, largest and smallest gap and overall discrepancies. Some of the results we have obtained are; the demonstration that of all uniform distributions, the hop model is the most even, and the random model the least even. We also have

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