# Quod Erat Demonstrandum

## 2010/04/23

### 一點心情

Filed under: NSS,School Activities — johnmayhk @ 12:05 上午
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## 2010/04/05

### 心在線上

L.U. 的一道舊題目，見下：

$y = m_1x + \frac{a}{m_1}$
$y = m_2x + \frac{a}{m_2}$
$y = m_3x + \frac{a}{m_3}$

## 2010/01/01

### 俄羅斯方塊帶給我們的生命教育…

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 12:38 上午
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## 2009/12/15

### 垂心的坐標

Filed under: Additional / Applied Mathematics,HKCEE,Junior Form Mathematics — johnmayhk @ 2:28 下午
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$A(x_1,y_1), B(x_2,y_2), C(x_3,y_3)$，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），

## 2009/11/03

### 不能秒殺的提問之在三角形內

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 12:43 下午
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## 2009/09/25

### Find dy/dx at a point not on the curve

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 4:50 下午
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When distributing the marked test paper to students, one student, Carman, reminded me that there was a ‘question’ in the following question:

If $x^3 - 4x^2y + 3xy^2 - y^5 = 10$, find $\frac{dy}{dx}$ at the point ($-2,1$).

Carman said, ‘the point does NOT lie on the curve.’

Good observation! I had to say thank you to him. Although I’m not the setter, I should bear the responsibility of checking the paper.

But a natural follow-up question turns up: what is the meaning of the number $\frac{dy}{dx}|_{(-2,1)} = \frac{31}{33}$ we are obtaining? Is the number meaningless or standing for something?

Let’s consider a simple example. (more…)

## 2009/08/30

### Finding general term by generating function

It is extremely easy to set up questions on number pattern, like

1, 3, 8, 19, 42, 89, ?

for more details, we may tabulate the question as:

the question is, when $n = 6$, what is the value of $a_n$?

My first reply to such kind of question is

“no need to do" (more…)

## 2009/08/23

### 等闊曲線 2

Filed under: HKCEE,mathematics — johnmayhk @ 12:28 下午
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「每一個角對面對應著一個圓弧；同樣，每一個圓弧對面也對應著一個角」 – – – – – – (*)

## 2009/08/10

### 等闊曲線 1

Filed under: Fun,HKCEE,mathematics — johnmayhk @ 9:32 下午
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## 2009/07/06

### 公平分配

Filed under: Junior Form Mathematics — johnmayhk @ 2:24 下午
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A.

B.

1961 (more…)

## 2009/04/28

### 有關圓形方程和軌跡的無聊討論

Filed under: HKCEE,mathematics — johnmayhk @ 4:28 下午
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【其一】 上課材料

To 4E students: you may download the worksheet (2009-04-24) at

together with some exploration at

【其二】 笑到喊

$x^2 + y^2 + Dx + Ey + F = 0$ – – – – – – (*)

$x^4 + 2x^3 + (2y^2 - 2y - 1)x^2 + (2y^2 - 2y - 2)x + y^4 - 2y^3 - y^2 + 2y + 1 = 0$

## 2009/03/29

### 大數值的乘階

$1! = 1$
$2! = 1 \times 2 = 2$
$3! = 1 \times 2 \times 3 = 6$
$4! = 1 \times 2 \times 3 \times 4 = 24$

$170! \approx 7.2574 \times 10^{306}$

## 2009/01/31

### 拉 curve

Filed under: Additional / Applied Mathematics,Junior Form Mathematics — johnmayhk @ 10:48 下午
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## 2009/01/10

### John 的心情仍然欠佳，為何？

Filed under: Life,mathematics — johnmayhk @ 3:15 下午
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A. 感到光榮
B. 沒有感覺
C. 感到憤怒（？）