Lecture

Elementary Operations in Geometry

In course

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Description

This lecture delves into the foundational concepts of geometry, exploring Descartes' contributions to the field and the transition from ancient geometric principles to modern algebraic operations. The instructor explains the significance of Euclidean geometry, focusing on the five algebraic operations on segments: addition, subtraction, multiplication, division, and square root extraction. Through detailed demonstrations, the lecture covers the construction of figures using ruler and compass, highlighting the limitations of constructible numbers and the development of more sophisticated algebraic theories. The lecture concludes with a discussion on transcendent numbers and the challenges of constructing certain geometric values, providing insights into the historical evolution of mathematical concepts.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_01yj55qy

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