微分幾何(英文:differential geometry)係幾何學嘅一個分支,用到微分、積分、線性代數同多重線性代數去研究幾何問題。
喺好多現實應用當中,人都要計幾何物體嘅表面面積同體積,對於好似球體、錐體同立方體等簡單基本嘅幾何物體,佢哋嘅表面面積同體積可以用相對簡單嘅方程式計,例如正方體嘅體積係
當中 係個正方體嘅邊有幾長(正方體定義上就係條條邊一樣咁長嘅)。
問題係,現實世界嘅物體好少可會咁簡單,例子可以睇吓文頭幅圖噉嘅曲面。微分幾何就可以解決呢啲問題。微分幾何用咗微積分嘅做法:簡化講,微積分技術可以將一條曲線想像成一條無限咁多條極細直線組成嘅線,再用積分方法計出條線下面包含嘅面積,進而幫手計塊曲面包嘅體積。
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