# Quod Erat Demonstrandum

## 2009/02/28

### [FW] 新聞耳目 : 古蹟殺手做校董 藝術學院扮保育

Filed under: Report — johnmayhk @ 7:38 上午

## 2009/02/27

### 兩個翦影

Filed under: Life,Report,School Activities — johnmayhk @ 12:10 下午

【其一】

## 2009/02/25

### 葉影微言

Filed under: Family,Life,School Activities — johnmayhk @ 12:06 下午

## 2009/02/24

### Minor point in differentiation

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 1:43 下午
Tags: ,

This is a simple question in differentiation.

Let $x^2 = \sqrt{y^6}$ for any real number $y$, determine $\frac{dy}{dx}$ at (1,-1). (more…)

## 2009/02/23

### .

Filed under: Family,Life — johnmayhk @ 6:19 下午

## 2009/02/20

### Some F.4 textbook questions

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 4:55 下午
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Students may find the following textbook questions difficult.

Question 1

Refer to the figure below, given that
$DE \perp AB$ and $DF \perp AC$;
$ED = a$;
$AB : AC = m$.

Show that $\tan\alpha = \frac{2m - 1}{\sqrt{3}}$. (more…)

## 2009/02/19

### Just an old question about F.4 trigonometry

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 9:55 下午
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It is glad that F.4 students asked me how to evaluate

$\sin1^o \times \sin2^o \times \sin3^o \times \dots \times \sin90^o$

Here is a way. (more…)

## 2009/02/18

### 未名湖是個海洋

Filed under: Life — johnmayhk @ 8:05 上午

## 2009/02/17

### Asymptotic Behavior of Solutions to Linear Equations

Apart from the interesting article in the last post, Justin also sent me the following interesting question:

Consider

$\frac{dy}{dx} + ay = Q(x)$ – – – – – – (E)

where the constant $a$ is positive and $Q(x)$ is continuous on [$0,\infty$). (more…)

## 2009/02/07

### [FW] Doing the Math to Find the Good Jobs

Filed under: Report — johnmayhk @ 7:26 上午

(Justin had forwarded the following article to me, may be mathematics lovers find it interesting.)

By SARAH E. NEEDLEMAN
Nineteen years ago, Jennifer Courter set out on a career path that has since provided her with a steady stream of lucrative, low-stress jobs. Now, her occupation — mathematician — has landed at the top spot on a new study ranking the best and worst jobs in the U.S. (more…)

## 2009/02/03

### [FW] 龔立人﹕我們等待聖本篤而不是先知

Filed under: Life — johnmayhk @ 4:46 下午

(明報)1月21日 星期三 05:05

【明報專訊】是否將同性同居伴侶納入《家庭暴力條例》（簡稱條例）受保障範圍是當下激烈（但可能不理性）辯論的焦點。反對將同性同居伴侶納入條例者認為這是間接將家庭定義，會為日後同性婚姻合法性鋪路。支持者卻認為同性同居伴侶應平等地得到條例保障，而這與爭取同性婚姻不應混淆。前者主要以某類基督宗教人士為主（例如蘇穎智牧師），後者包括基督宗教人士、人權倡導者、法律學者、性小眾等等。本文不是要評論他們的差異和探討其他可能性，而是嘗試分析反對者中某類基督宗教人士由恐懼而建立的理性和行動，從而思考基督宗教的社會角色。 (more…)

## 2009/02/01

### 卡爾松（Carleson）不等式

Filed under: Pure Mathematics — johnmayhk @ 9:25 下午
Tags: , , ,

Carleson first inequality

Let $a_1, a_2, \dots , a_n \in \mathbb{R}$, then

$(a_1 + a_2 + \dots + a_n)^2 < \frac{\pi^2}{6}(a_1^2 + 2^2a_2^2 + \dots + n^2a_n^2)$

Carleson second inequality

Let $a_1, a_2, \dots , a_n \in \mathbb{R}$, then

$(a_1 + a_2 + \dots + a_n)^4 < \pi^2(a_1^2 + a_2^2 + \dots + a_n^2)(a_1^2 + 2^2a_2^2 + \dots + n^2a_n^2)$