WEBVTT

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喺彼思，我哋做嘅就係講故事

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但係有個故事冇乜人講

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就係製作電影嘅時候

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我哋會幾常用到數學

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你初、高中學到嘅數學

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彼思成日都會用到

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我哋就由一個簡單嘅例子講起

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有冇人認得佢 （歡呼聲）

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係呀，反斗奇兵嘅胡迪

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我哋試下叫胡迪，行過個舞台

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由左至右，好似咁

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信唔信都好，頭先你睇到咗好多數學

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喺邊呢？

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我哋首先要明白

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藝術家同設計師

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係用圖形同圖像來諗嘢

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而電腦就係用數字同方程式來諗嘢

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為咗連繫呢兩個世界

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我哋要用一個數學概念

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叫坐標幾何

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我哋會用個坐標系統

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用 x 表示要向右行幾多

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用 y 表示要去幾高

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有咗呢啲坐標，我哋就可以

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無論幾時，都即刻講明胡迪喺邊

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就好似我哋知道

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喺左下角幅圖嘅坐標

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咁就知淨低幅圖喺邊

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頭先見到嗰小小滑動嘅動畫

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我哋叫呢個動作做平移

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x 座標值會由 1 開始

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去到大約 5 就停

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如果我哋用數學嚟寫

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最尾個 x

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就大個開頭個 x

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所以，平移嘅公式

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就係加法

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係咪？

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咁縮放呢？

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就係令一樣嘢變大或者變細

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估下縮放用咩數學？

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擴大、乘法，冇錯啦

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如果你要令一樣嘢變大兩倍

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你要將 x 同 y 嘅坐標

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全部乘 2

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所以，縮放嘅數學

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就係乘法

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明唔明？

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咁呢個呢？

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旋轉又點？轉嚟轉去

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旋轉嘅數學就係三角函數

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呢到有個公式可以用嚟表達

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初初睇會有啲得人驚

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你可能喺中二或者中三時學過

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如果你學緊三角函數

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諗到底幾時會需要用到呢啲嘢

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你就記住，喺我哋任何一套戲入面

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任何嘢旋轉

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背後就有三角函數啦

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我中一嗰時愛上咗數學

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有冇人喺中一呀？有幾個？

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我中一班嘅科學老師畀我睇過

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點樣用三角函數

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計算我整緊嘅火箭會飛到幾高

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我覺得好神奇

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從此就愛上咗數學

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呢啲數學有啲古老

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我哋都認為

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數學係由好耐以前嘅
古希臘人發明嘅

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傳聞就係

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有趣嘅數學已經全部畀研究晒啦

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又或者，所有數學都已經畀諗晒出来

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但事實係，新嘅數學

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仲係無時無刻咁被創造

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有啲係喺彼思度創造出嚟嘅

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我想畀個例子你哋

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呢度有啲我哋早期嘅電影角色

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《海底奇兵》、
《怪獸公司》、《反斗奇兵 2》

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有冇人識左上角個藍色角色？

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係多莉，好容易睇出来

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問條難少少嘅

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有冇人識右下角嘅角色？

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「艾爾玩具城」老闆「艾爾」，啱

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呢啲角色

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佢哋其實真係好複雜

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啲形狀好複雜

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比如話個玩具清潔員

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中間嗰個

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呢隻係佢隻手

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帶佢過機場保安

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就真係夠晒好玩

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隻手嘅形狀真係好複雜

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唔只係一堆球體和圓柱體黐埋

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唔只佢本身複雜

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連佢移動嘅方式都好複雜

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我同你講下，我哋係點做到嘅

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首先，要講下重點係咩先

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呢到有兩點，A 同 B

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兩點中間有一條線

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我哋要由二維開始

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中點 M 喺呢度

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將條線平分

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呢個就係幾何學

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要寫成方程式同數字

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我哋再次用個座標系統

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如果我哋知 AB 嘅座標

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我哋就計到 M 嘅座標

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用平均法就得啦

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知道呢哋嘢， 已經夠你喺彼思做嘢

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我展示畀你睇

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我要做一樣有少少得人驚嘅嘢

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喺到做個現場示範

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我有個四角形喺到

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我係要令佢

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有圓滑嘅曲線

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而我淨係用中點就做到

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首先，我會做一個

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叫做分割嘅操作

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即係將所有嘅邊加上中點

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4 個中點就變到 8 個點

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但係條線仲未夠圓滑

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我要令佢圓滑多少少

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將呢啲點移去

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原本位置順時針隔籬線嘅中點

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做個動畫畀你睇

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我會叫佢做平均步驟

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咁宜家我有 8 點

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佢哋圓滑咗少少

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我要成條圓滑嘅曲線

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咁我要點做

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再嚟一次，分割同平均

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咁宜家我就有 16 點

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我會將分割同平均呢兩個步驟

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合成一樣

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就叫做細分嘅嘢

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即係分割之後再摞平均值

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宜家我有 32 點

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如果仲未夠圓滑，我就再整

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就會有 64 點

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見唔見到呢個更圓滑嘅曲線

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來自呢哋原來嘅點

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我哋就係咁創造我哋嘅角色嘅外型

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但記住，我頭先講咗

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淨係了解靜止嘅形狀

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固定嘅形狀係唔夠嘅

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我哋要令佢郁起身

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而要郁呢啲曲線

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就係細分最勁嘅嘢

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見過《反斗奇兵》入面嘅三眼仔？

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你知佢哋會咁叫

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「噢」準備好未？

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咁我哋要郁呢啲曲線呢

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好簡單咁郁原本嗰 4 點

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「噢」

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好，我覺得咁好勁

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如果你唔覺嘅，門口就喺嗰邊

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因為冇得再勁啦

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分割同平均嘅概念

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適用於所有表面

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所以分割，平均

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分割，平均

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放埋一齊去細分

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咁我哋就創造到

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所有嘅人物嘅3D 外型

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細分呢個概念

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喺 1997 年一套叫《棋局》嘅

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短動畫度首次採用

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主角基里後尾有喺
《反斗奇兵2》度客串

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佢就係嗰個玩具清潔員

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佢嘅兩隻手

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就係我哋第一次用細分整嘅

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每隻手都係細分嘅表面

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佢塊面係細分嘅表面

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佢件外套都係

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呢隻係佢細分前隻手

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呢隻係佢細分後隻手

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所以細分將

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所有表面都整到平滑晒

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創造咗你喺螢幕同戲院

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睇到哋咁靚嘅表面

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嗰次之後，我哋就一直咁樣創造人物

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呢個係《勇敢傳說》嘅主角梅蘭達

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佢條裙係細分嘅表面

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佢對手、佢塊面

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全部族人嘅面同手

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都係細分嘅表面

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今日我哋講到加法、乘法

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三角函數同幾何點樣喺電影裡邊應用

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如果我有多少少時間

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我就可以畀你睇到線性代數

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微分同積分

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起到嘅作用

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今日我最主要係想你哋知道

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你哋宜家所學到嘅所有數學

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高中到大學二年級嘅

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每一刻、每一日，喺彼思都會用到

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多謝