非數學類，不喜勿入。 (more…)
July 11, 2009
July 8, 2009
July 6, 2009
公平分配
A.
小學一年級 IQ 題：如何公平地把 4 個橙公平分給 7 個小朋友？
答曰：哼，用搾汁機啦！（有 D 似「愛『夫』堅」廣告 …）
B.
開心 share 一個童年片段，是公平分配的反面教材，不知我的弟弟記得否？
話說 N 年前某天，某某送了一粒瑞士糖給我和弟弟，注意，係一粒（點解唔送多粒？）。因為粒糖好硬，刀不能分；於是我告訴弟弟：「等我咬一半畀你啦。」弟弟一直站在我旁，等呀等…等了很久…我還沒有分一半給他，出事！因為我一路咬下咬下，唔覺唔覺冇o左件事，成粒食曬！之後點？忘記了。 (more…)
July 4, 2009
July 3, 2009
= ?July 2, 2009
表達成二進制的數字。
如何轉成二進數？這個也簡單，
如何轉成二進數？ June 26, 2009
或 
？ June 23, 2009
[FW][Song] No choice, I’ll be
It was a love so big that it filled his heart
Til it swelled and finally burst apart
And where the love spilled out they called it art
But he never really had no choice
Whoa, he had no choice
No, he never had no choice
When he gave his river a voice
He never really had no choice.
He was thinking that the pain came much too soon
When he locked himself up inside his room
Well it hurt real bad to write that tune
but he never really had no choice
And there were some who could not understand
When he built those castles with his hands
And he knew damn well they were only sand
But he never really had no choice.
Whoa, he had no choice
No, he never had no choice
When he gave his river a voice
He never really had no choice.
Sometimes a man sometimes a boy
And he made some music and he made some noise
But he felt his pain and he felt his joy
But he never really had no choice.
There was a beautiful fire inside of him
As he balanced his way out on that limb
Could of burned right through that branch so thin
but he never really had no choice
Whoa, he had no choice
No, he never had no choice
When he gave his river a voice
He never really had no choice.
And they all talked about him when he died
They studied and they theorized
But when he was through they’d laughed and cried
And he never really had no choice
It was a love so big that it filled his heart
‘Til it swelled and finally burst apart
Where the loved spilled out they called it art
But he never really had no choice
Whoa, he had no choice
No, he never had no choice
When he gave his river a voice
He never really had no choice.
Whoa, he had no choice
No, he never had no choice
When he gave his river a voice
He never really had no choice.
================================================
Another beautiful song by Edwin Mccain: I’ll Be
Enjoy and think.
June 22, 2009
考試前後
前
考中二數學前夕，梁同學致電問數。我都「好野」，一邊行街赴父親節宴會，一邊做數講數。
問題太多，晚上回家，梁同學再問下半場。
他問什麼中二數學問題？列幾個：
1. Factorize 
2. 把 8 cm * 10 cm 長方形一對角（opposite angles）摺疊，求摺痕長度。
3. 二進制轉和十六進制的直接互換方法。
…
等等。
後 (more…)
June 21, 2009
應用純數
有人強調數學在生活中的應用，有人指出所謂「數學在生活中的應用」是牽強的。經驗使我比較贊成後者。
無論如何，以趣味的角度向學生介紹（所謂的）數學在生活中應用的例子，或許可以達到某些教學的成效。
讓我在這裡介紹一個「偽應用」吧，起碼三本數普書籍有記載此例。
修純數的同學定會接觸介值定理：
設 f 為定義在 [a,b] 上的連續函數，已知 f(a)f(b) < 0，則在 (a,b) 內存在 c 使 f(c) = 0。
這個定理有沒有生活應用例子？嗯，或許有，見下：
今有方桌子一張，四條腿等長。若把桌子放於凹凸不平但平滑的地面上，證明一定存在某個位置，使四條腿同時著地。 (more…)
June 18, 2009
June 16, 2009
June 14, 2009
捐血頒獎禮
今天是香港紅十字會輸血服務中心 2009 年度捐血頒獎典禮暨慶祝世界捐血者日（6 – 14），因為學校得了獎，我出席於香港紅磡海逸皇宮大酒樓舉行的典禮。
李錦強先生捐血次數累計：425 次（注：指的是成份捐血，每年可以捐 20 多次），相當厲害。
大會邀請了幾位長期捐血者分享感受，其中 Mr. Halliday 的分享也很有趣。
擠滿出席者的典禮上，雖然除了經常到校的收集血液的職員護士，和主禮嘉賓保安局局長李少光，全是陌生面孔，感覺不太「孤單」，因為我「假假地」也和紅十字會有一點連繫，也算是團體的一員。
因太太約我，我待頒發全部獎項後，沒有享用大會安排的午膳，便逃了。
拍了捐血寶寶，給兒子看，也和大家分享：
為打發時間，帶了數學書看了看，希望有機會又分享一下。
June 12, 2009
June 11, 2009
June 8, 2009
June 7, 2009
[FW] 在大自然中窺見費伯納契數列
http://sa.ylib.com/saeasylearn/saeasylearnshow.asp?FDocNo=1389&CL=81
－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
全國奈米科技應用競賽 ：
http://www.bme.nchu.edu.tw/competition/
（頗有趣。香港有沒有類似的比賽？）
June 4, 2009
溫書題
這是溫書時期。
1. 有關數列的題目
這是校內 2007-2008 年度純數期終試其中一題：
=======================================
Let {
Let 
Show that 
======================================= (more…)
June 1, 2009
[FW] LOL – Law of love
Universal Law Of Love:
“Love Can Neither Be Created Nor Be Destroyed; Only It Can Transfer From one Girlfriend To Another Girlfriend With Some Loss Of Money ” (more…)
May 30, 2009
WolframAlpha
Gower 介紹了 WolframAlpha，值得推介：
比如要找 3^100 的頭十個位，又或是在 1000 至 2000 內的所有質數，全不費力。我略略在其網頁輸入：
the first 10 digits of 3^100
prime numbers between 1000 and 2000
euler constant
napier number
100 digits of e
200 digits of pi
…
立即得出解答，數學人應該用得著。
May 23, 2009
。無論擲兩顆，三顆，它們的點數期望值皆是 
，故此，兩個點數差的期望值就是 
。 May 15, 2009
幾何舞術
Source: metropop 154
未想過可以如此 crossover，這三樣都喜愛，但時間不許我做太多「無謂野」…
Details: (看看當中的 video)
http://www.frenchmay.com/posts/program_detail/91
May 13, 2009
May 12, 2009
.May 11, 2009
[FW][News] 豆腐渣奪去完美女兒 「等待真相」
(明報)2009年5月10日 星期日 05:05
【明報專訊】Angel一直沒有忘記劉小英與富新母親們，劉小英則一直念念不忘亡女畢月星，「她在我心中是最完美的，豆腐渣把她奪去了，我每天晚上都夢見她回來，我們還欠一個公道！」 (more…)
May 10, 2009
[FW] 向社會推薦優良數學科普書籍
http://www.math.sinica.edu.tw/mrpc_jsp/book/about.jsp
同學，有時間看看短短的書介，找有興趣的題目深入研究研究吧！
May 7, 2009
是有理數還是無理數，我真是答不出來 May 6, 2009
2009 CE Additional Mathematics Paper Section B
重點題目：
以下是 2009 CE Additional Mathematics Q.18，同學，看看你可否在 16 分鐘內正確地完成它：
The following figure shows a park AED on a horizontal ground. The park is in the form of a right-angled triangle surrounded by a walking path with negligible width. Henry walks along the path at a constant speed. He starts from point A at 7:00 am. He reaches points B, C and D at 7:10 am, 7:15 am and 7:30 am respectively and returns to A via point E. The angles of elevation of H, the top of a tower outside the park, from A and D are 45
(a) Express DK in terms of h. (1 mark)
(b) Show that AB = h
(c) Find the angle of elevation of H from C correct to the nearest degree. (3 marks)
(d) Henry returns to A at 8:10 am. It is known that the area of the park is 9450 m
(i) Find h.
(ii) A vertical pole of length 3 cm is located such that it is equidistant from A, D and E. Find the angle of elevation of H from the top of the pole correct to the nearest degree. (5 marks) (more…)
April 29, 2009
純數小技
一．Chain rule 秘技：不要忘記「D 那星」
在下師承我的啟蒙中學教師馬 sir，他喜歡用星星 
不妨視 
April 28, 2009
有關圓形方程和軌跡的無聊討論
【其一】 上課材料
To 4E students: you may download the worksheet (2009-04-24) at
f4-additional-mathematics-worksheet-20090424
together with some exploration at
【其二】 笑到喊
形如下式的二元二次方程
中四的同學知道，其圖像代表著圓形（指實圓圓周 circumference of real circle）。
現在反過來，代表著圓形的方程式，是否一定形如 (*)？（即二元二次）
不一定，以下是一條二元四次方程方程
其圖像，也是圓形。為何？ (more…)
April 27, 2009
2009 CE Mathematics Paper
今天考會考數學，同事看卷後，感到題目很淺，考生出來，紛紛說「太淺了，怕取不到 A」云云。
聊舉數例
2009 CE Mathematics Paper I Q.17
Given
A, B, C and D lie on the horizontal ground. CE is perpendicular to the plane ABE.
AC = 28 cm, BC = 25 cm, BD = 6 cm, BE = 24 cm, 
Find the shortest distance from E to the horizontal ground. (more…)
April 22, 2009
一些有關不能使用 l’Hôpital’s rule 的例子
昨天和同事討論 l’Hôpital’s rule，我就是忘記了一個例子，以說明就算運用 l’Hôpital’s rule 找到 
April 21, 2009
Trivial reflection of mathematics teaching
Pure Mathematics is a subject of mathematical “techniques”. It provides students with certain tools and procedures to solve certain mathematical problems.
However, for me, Pure Mathematics is a subject of “art”.
“Techniques” can be taught, while “art” cannot be taught easily. (more…)
April 20, 2009
Just reply to my so-called ETV
Here is just a reply to my primary school mathematics ETV (magic square).
When I was a primary school boy, my mathematics teacher taught us how to construct magic square, today, I still remember what she had taught me. For your reference, here is an easy way to construct magic square of odd order:
http://en.wikipedia.org/wiki/Magic_square#A_method_for_constructing_a_magic_square_of_odd_order
Students, try to construct magic squares (more…)
April 19, 2009
April 17, 2009
可導性
這是有關「可導性」（differentiablity）的討論，寫給那天沒有上復活假期補課班的中六同學。注：討論純粹以中學數學的觀點出發。
先請同學回答下面三道是非題：
1. Put 
2. If 
3. If 
April 15, 2009
純數生活例子（無聊篇）
中四數學教科書中，有關於圓的切線（tangent）之主題，當中舉了一個「生活例子」：太陽從海面初升，代表了圓形交直線於兩個不同點；當整個圓形剛剛從海面出現，就是直線切圓於一點的情況云云。 (more…)
April 14, 2009
家庭小片段-0009
記一些片段而已。
家近山，附近很容易找到昆蟲。太太捉了一些，諸如飛蛾，蜘蛛，臭蟲等等做兒子的「學具」，有一些昆蟲已經給了幼稚園老師。2009-03-30，我和太太捉了一隻小班蟬（已是第三隻了，之後捉了一隻大蝴蝶），非常高興可以和兒子上生物課，見下： (more…)
