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東海科學

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篇名 淺談「冰上幾何學」
卷期 23
並列篇名 Geometry on Ice: a brief exploration
作者 胡馨云
頁次 019-031
關鍵字 花式滑冰參數方程式數值積分插值法figure skatingparametric equationsnumerical integrationsinterpllationTSCI
出刊日期 202207

中文摘要

本篇短文中作者將花滑這項令人喜愛的運動與數學做一個巧妙的連結。分享幾個概念給讀者,首先,花滑中一些精彩美妙滑行或組合旋轉動作其實是遵循著一些你我熟知的曲線,文中將會簡單介紹這些有趣的曲線。再者是透過數值積分法協助估算出花滑選手在表演節目中體能消耗的情況,此與軌跡總長有關。第三點則是想藉由插值法的概念透過電腦程式來編排幾種連續平滑的滑行,而後再來進行冰上實體練習。這樣一來可大幅減少運動員不必要的體能消耗及意外受傷。最終希望偏愛運動方面的讀者用欣賞的角度來了解數學知識的力量。另一方面,對於偏好數學的讀者可意識到諸多體育項目使用了曾學習過的數學知識,抽象的方程式也能應用到日常的生活中啊!

英文摘要

In this article, the author makes a close connection between the popular sport of figure skating and mathematics. In an attempt to describe the fundamental concepts to the readers, we first relate a few well-known and commonly used mathematical functions to the wonderful skating path and combinational spins patterns. We show that the motions of skating can be described through the control parameters in the mathematical curves. In this article, a few interesting curves are introduced for describing the figure skating paths. We then show that the energy consumption of the skaters can be calculated by integration, which is related to the total length of the skating path. Thirdly, we show how the skating motion can be simulated by numerical approximation and interpolation, and this computer simulation can be used for skating training of the figure skaters. The computer simulation can help to estimate the physical energy consumption of the figure skaters in the performance program, and minimize the unnecessary physical exertion and accidental injuries of athletes. It is hoped that this study provides an illustration on the useful application of mathematics to sports. For those with passions in mathematics, it shows that the previously learned mathematics can be used to enhance the athletic trainings, and how some abstract mathematical equations can be easily applied to our daily life.

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