# Quod Erat Demonstrandum

## 2009/12/31

### 新年警示與願望

Filed under: Fun — johnmayhk @ 10:55 下午

## 2009/12/18

### Did you know?

Filed under: Report,School Activities — johnmayhk @ 9:37 下午

### [FW] BARCELONA en 1908

Filed under: Life — johnmayhk @ 10:38 上午

## 2009/12/15

### 垂心的坐標

Filed under: Additional / Applied Mathematics,HKCEE,Junior Form Mathematics — johnmayhk @ 2:28 下午
Tags: ,

$A(x_1,y_1), B(x_2,y_2), C(x_3,y_3)$，易知 $\Delta ABC$ 形心／重心（centroid）的坐標為

$G(\frac{x_1 + x_2 + x_3}{3} , \frac{y_1 + y_2 + y_3}{3})$

$\overrightarrow{OG} = \frac{\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC}}{3}$

（初中同學試以 section formula 證之）

$\Delta ABC$ 的外心（circumcenter）為 $O$，並以 $O$ 為直角坐標系的原點（origin），

## 2009/12/11

### 平移與求導

$f(x) = ax^4 + bx^3 + cx^2 + dx + e$

$f(x + L)$
$\equiv ax^4 + (4La + b)x^3 + (6L^2a + 3Lb + c)x^2$
$+ (4L^3a + 3L^2b + 2Lc + d)x + (L^4a + L^3b + L^2c + Ld + e)$ (more…)

## 2009/12/04

### 記中四（高中一）某無聊數學片段

Filed under: Fun,NSS — johnmayhk @ 9:25 下午

Let $\alpha, \beta$ be roots of $7x^2 - 4x - 3 = 0$ ($\alpha > \beta$). Find the values of

(a) $\alpha - \beta$;
(b) $\alpha^3 - \beta^3$;
(c) $\frac{\alpha}{\beta^2} - \frac{\beta}{\alpha^2}$.