仲有一個
Why radius is perpendicular to tangent at the point of contact
Just a result from vector calculus that, using dot product in circular motion:
r‧r' = 0
Where r' is the first derivative of r
如果係中學生問你呢個問題呢
一樣用vector cal拋鳩佢
所以數理化卷必須要設立 bonus 常識題去西走考試機器
太抽象
對我實際生活生存無直接關係
抽象嗰度，係咪例如一句描述一個圖形嘅句子，你想像唔到個圖形?
無直接關係……等同無興趣喔?
三角嗰D sin 2a = 一抽乜鬼 之類咪死記硬背囉， 老實講prove 左點黎都唔會記得住
compound angle formulae 好似係由 cos(x+y) 開始用 polar coordinate prove
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
中學嘅數好多都可以自己推出嚟
好多學生掛住盲目操數唔溫書
無理過嗰課本身講啲乜
自然覺得難記
呢啲人一上到中四即刻出事
Just call an arts stream student to explain:
For an equation x^2 + ax + b=0 where a and b are integers.
Explain why when the roots are all complex, b>0.
其實點解sum of root係a+b , product of root係ab , 教科書似乎一直以嚟都冇解釋過
呢個有咩好解釋
要解嘅係Sum of roots = -b/a
仲有product of roots係c/a，點解?
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
咁咪直情玩死埋啲science仔
下下都要mathematical proof 淨係俾你地Phys maths佬讀得啦
利申：由calculus開始無視哂啲proof
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
咁咪直情玩死埋啲science仔
下下都要mathematical proof 淨係俾你地Phys maths佬讀得啦
利申：由calculus開始無視哂啲proof
無讀過proof就唔好話自己讀數學
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
咁咪直情玩死埋啲science仔
下下都要mathematical proof 淨係俾你地Phys maths佬讀得啦
利申：由calculus開始無視哂啲proof
無讀過proof就唔好話自己讀數學
無話自己讀過calculus
如果唔係maths compu應該好多人揀唔讀
仲有一個
Why radius is perpendicular to tangent at the point of contact
Just a result from vector calculus that, using dot product in circular motion:
r‧r' = 0
Where r' is the first derivative of r
如果係中學生問你呢個問題呢
一樣用vector cal拋鳩佢
太抽象
對我實際生活生存無直接關係
太抽象
對我實際生活生存無直接關係
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
咁咪直情玩死埋啲science仔
下下都要mathematical proof 淨係俾你地Phys maths佬讀得啦
利申：由calculus開始無視哂啲proof
無讀過proof就唔好話自己讀數學
無話自己讀過calculus
如果唔係maths compu應該好多人揀唔讀
dse core 要玩proof唔會好難,不過耐冇用就會唔記得點prove。我中學連proof都明埋。
Calculus 我都無視哂d proof, 知咩情況做咩但再深入就唔知。坦白講，yr1 d in 你識做真係夠做,佢又唔會問到好深入。讀緊surface integral, multiple integral , div thm etc, d proof 煩左睇都唔想睇，知點用同點做就算。
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
咁咪直情玩死埋啲science仔
下下都要mathematical proof 淨係俾你地Phys maths佬讀得啦
利申：由calculus開始無視哂啲proof
無讀過proof就唔好話自己讀數學
無話自己讀過calculus
如果唔係maths compu應該好多人揀唔讀
dse core 要玩proof唔會好難,不過耐冇用就會唔記得點prove。我中學連proof都明埋。
Calculus 我都無視哂d proof, 知咩情況做咩但再深入就唔知。坦白講，yr1 d in 你識做真係夠做,佢又唔會問到好深入。讀緊surface integral, multiple integral , div thm etc, d proof 煩左睇都唔想睇，知點用同點做就算。
non math major既話根本冇所謂
一知半解就得
講多句
dse core以至小學數學既proof根本一d都唔容易
Funny questons:
Why volume of sphere (4/3)pie r^3?
Why surface area of sphere is 4pie r^2?
Is it a coincidence that surface area of sphere is the derivative of its volume?
Volume: Use polar coordinate to do double integration.
Surface area: Out of post-2005 HKAL Pure Math Syllabus
就好似咁 唔係話要你背唔理解
但係唔通你叫個中二學生理解咩係d in？
背式快好多囉 下下都講理解要記多幾多野
責任上係要同佢講呢舊嘢有得解
但唔係中二程度做到嘅事
總之唔可以俾學生覺得呢啲嘢係好似science咁用實驗verify到就當係
咁咪直情玩死埋啲science仔
下下都要mathematical proof 淨係俾你地Phys maths佬讀得啦
利申：由calculus開始無視哂啲proof
無讀過proof就唔好話自己讀數學
無話自己讀過calculus
如果唔係maths compu應該好多人揀唔讀
dse core 要玩proof唔會好難,不過耐冇用就會唔記得點prove。我中學連proof都明埋。
Calculus 我都無視哂d proof, 知咩情況做咩但再深入就唔知。坦白講，yr1 d in 你識做真係夠做,佢又唔會問到好深入。讀緊surface integral, multiple integral , div thm etc, d proof 煩到睇都唔想睇，知點用同點做就算。
non math major既話根本冇所謂
一知半解就得
講多句
dse core以至小學數學既proof根本一d都唔容易
如果有個網 集齊晒由古至今
數學家嘅論文就好 好想狂煲晒佢
如果有個網 集齊晒由古至今
數學家嘅論文就好 好想狂煲晒佢
Google scholar..
有啲太舊只有paper work
或者無英文版。。。
