幾何學賞析|丘成桐院士

中央研究院Academia Sinica June 26, 2017
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中央研究院Academia Sinica

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歡迎來到中央研究院影音頻道!🎉 為使學術研究發揮社會教育功能,激發年輕學子與社會大眾的求知熱情,本頻道主要提供各類科普知識影片,例如本院定期舉辦的「知識饗宴」及「故院長講座」科普演講,特邀本院院士或各領域研究人員主講,以深入淺出、生動詳實的表達方式,介紹本院的各項研究成果;並經常結合中研院官方臉書,進行線上影音直播,服務未能前來院內聽講的各地民眾,也能有如臨現場的感受及即時學習的機會。 另外,亦不定時推出各項院內外各項活動紀錄,例如外縣市科普演講、本院最新簡介、數理、生命及人文各組研究人員訪談及院區開放活動花絮等影片。🌍🎥🔬 Welcome to the Academia Sinica YouTube Channel! 🎉 Dive into a world of discovery with our diverse collection of popular science videos, where we share cutting-edge research and aim to ignite your curiosity. Here, you'll find a treasure trove of science content, from videos and livestreams of our exciting science events like the Open House events, Knowledge Feast series, and Popular Science Lectures, to in-depth interviews with our brilliant researchers. Join us as we explore the frontiers of knowledge and bring the wonders of science closer to you! 🌍🎥🔬

Video Description

101年蔡元培院長講座 講題:「幾何學賞析」 時間:100年12月31日 主講人:丘成桐院士(美國哈佛大學數學系教授兼系主任) 主持人:本院彭旭明副院長 摘要: 古人在生活實踐中,發現了某些簡單的幾何圖形滿足了一定的規律。這些規律簡潔明瞭,具有一種美感!令人驚歎。這些幾何性質,在希臘文明中得到明確推崇。 柏拉圖發現只有五種正多面體,也提出了三個著名的幾何問題,歐幾裡德集當時幾何學的大成,用五條公理推導大量有趣的命題,實開千古科學演繹法之先河,直接影響到以後牛頓的力學體系。 大部分學者認為統禦自然界的共通原理必須簡潔,這種觀念或起源於希臘的基本精神,希臘人是視美與善、身與心、個人與國家、神與人是調和統一的。調和的思想也可說貫穿了古代數學直到近代數學的發展,從宇宙的起源,星球的運行,原子的結構,一直到山水人物的繪畫都有許多幾何學家參與其中,進行研究,做出了基本的貢獻,而「對稱」是幾何學裡一個極為重要的概念,也是調和觀念的另一表示。 幾何學的基本觀念和對幾何學的欣賞是隨著時代來變遷的,十九世紀初黎曼空間讓我們理解到空間的內在美。為了描述動場,Einstein指出黎曼空間應當隨時間改變,這個改變由Einstein場方程來主宰。動態幾何的美比靜態的美來得深入,但也因此更難以掌握。量子力學出現以後,幾何學得出一個新的工具,Dirac運算元使幾何學家迷茫,它解決了很多重要的幾何問題。造物的宏偉和瑰麗,可以從物理學和幾何學的關係看得出來。

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