In diploma thesis, we investigate the ratio of circumference and diameter of a circle in the Euclidean plane. Firstly we define a metric as a function for measuring distances and introduce a few special cases of metrics beside the already known Euclidean one. We present the taxicab metric, maximum metric, and p-metric. In the next part we show how to calculate the arc length of a curve in Euclidean space with geodesic approximation method and usage of Lagrange theorem. The main part consists of calculating the value of pi in different metrics using the formula for circumference of a circle and the arc length. In conclusion, we prove that the value of pi is actually minimal in the Euclidean metric.
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