自然科學中的數學概念

Abstract

我們利用自然科學中一些週期性運動及雙螺旋排列的現象，比較不同情況下軌跡的特性。利用不同參數的彈子球檯及李賽羅圖形探索有理數、無理數、同餘及完全剩餘系的關係。並利用雙螺旋圖形研究輾轉相除法、漸近分數與黃金比例的概念。透過自然科學系統的視覺化呈現，我們希望學習者可以更欣賞並學習更進一步的自然科學與數學。

We use some natural phenomenon as the periodic motion and the dual-spiral phyllotaxis picture to contrast the different behavior of their curve. Explore rational, irrational number, Residues and complete residue system by the billiards and the lissajous pictures with different value of parameter. Use the dual-spiral graphs to study the relation between the approximating fractions and the golden number. Through visualizing the character of natural system, we wish students can better appreciate the distinction and come to gain more sophisticated intuitions about natural science and mathematics.