我們從尤拉數e談起，試著以電腦為我們實驗的工具，利用數學軟體Mathematica 計算繪圖的功能，來激發我們自由而又豐富的想像力。這提供了我們兩個強有力的猜測。 對每一個猜測，我們先分析它的結構，然後試圖予以證明。第二個猜測，就是所謂的 Stirling公式。我們由此談到Gamma函數及其三種不同的界定方法。利用第三種界定的方 法，我們證明了Stirling公式。最後，我們用這些結果來決定Stirling公式中的常數[]做 為這篇文章的結束。 The Euler's number e brings us up a demonstration for the experimental nature of mathematics. The tool is a PC armed with the powerful mathematics package MATHEMATICA. Stimulated by such lively and interesting activity, we get two conjectures. We analyse the structure of each and then try to prove it. The second one is the so-called Stirling's formula. At this point, Gamma function comes in. We look at three distinct characterizations of the Gamma function. The third one gives us a new way to prove Stirling's formula. From this result, we conclude this paper by determining Stirling constant [] in a very simple way.
