自行車的制約與Menzin猜想

Abstract

先討論自行車運動時前後輪應有的關係，以及測面儀的應用。這兩者的運動模式都依循著「自行車制約」，但它們運動的結果卻有著截然不同的現象。Menzin為造成不同現象的原因提出了一個猜想。最後來討論這個猜想，證明在前輪走凸封閉曲線的狀況下的個猜想是對的。

First we compare how a bicycle behaves with how a Prytz planimeter works. A planimeter is an instrument that used to measure the area bounded by a closed curve. There are many type of planimeters, while the Prytz planimeter works the same as a bicycle, but has a totally different phenomenon. Menzin characterised these phenomenon. We also prove the Menzin's Conjecture under a special case that the front wheel moves in a convex closed curve.