# Quod Erat Demonstrandum

## 2009/09/05

### 會議補充二則

Filed under: Additional / Applied Mathematics,HKALE,University Mathematics — johnmayhk @ 11:32 下午
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1.

“Introduction to Topological Manifolds" by John M. Lee

2.

A, B, C, D start moving at four vertices of a square in a way that A moves toward B, B moves towards C, C moves toward D and D moves toward A always at uniform speed. Determine the locus of A.

$A$ 處於 ($x,y$)，則 $B$ 處於 ($y,-x$)。

$A$ 的軌跡。

$\frac{dy}{dx} = \frac{y - (-x)}{x - y} = \frac{x + y}{x - y}$
$y|_{x = a} = a$

$u = \frac{y}{x}$，得

$\frac{1 - u}{1 + u^2}du = \frac{dx}{x}$

$\tan^{-1}(\frac{y}{x}) = C + \ln{\sqrt{x^2 + y^2}}$

$\tan^{-1}(\frac{y}{x}) = \frac{\pi}{4} + \frac{1}{2}\ln{\frac{x^2 + y^2}{2a^2}}$

## 2 則迴響 »

1. Introduction to Topological Manifold這本書是屬於數普書藉嗎?
現在上分析課也開始接觸topology了。

迴響 由 Justin — 2009/09/08 @ 12:25 上午 | 回應

• Justin,

那本書的頭一篇，即我貼在文中的十數頁或許可算是「數普」吧。你可以學習 topology（是 point-set topology 嗎？），幸福呀，好好學習吧；有什麼有趣的東西，歡迎在此分享分享。

迴響 由 johnmayhk — 2009/09/08 @ 8:39 上午 | 回應