Lecture

Duplication of the Cube

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-124: Geometry for architects I

Ce cours entend exposer les fondements de la géométrie à un triple titre : 1/ de technique mathématique essentielle au processus de conception du projet, 2/ d'objet privilégié des logiciels de conception paramétrique 3/ de composante à part entière de l'h ...

Description

This lecture explores the historical problem of duplicating the cube, a complex mathematical challenge faced by ancient Greek mathematicians like Hippocrates of Chios. It delves into the construction methods attributed to figures such as Nicomedes and Plato, examining the use of different instruments to solve the problem. The lecture also discusses the concept of double mean proportionality and its significance in geometric constructions, as well as the misattributions of mathematical methods to historical figures like Plato. Various historical texts and geometric diagrams are analyzed to understand the evolution of mathematical problem-solving techniques.

Instructor

Bernard Cache

Official source

Related concepts (32)

Applied mathematics

Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.

Mathematics

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.

Mathematics education

In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge. Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods.

Mathematical model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).

History of mathematics

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.

Related lectures (64)

Cube Duplication: Geometric Insights

Explores the historical and mathematical significance of duplicating the cube and its geometric implications in ancient times.

Elliptic Problems

Covers the concept of elliptic problems and their applications in various scenarios.

Geometric Meanings: Euclidean Division and Divine Proportion

Explores the historical and mathematical significance of Euclidean Division and the Divine Proportion in geometry and art.

Optimal Transport: From Theory to Applications

Explores the history, theory, and applications of optimal transport in various fields, showcasing its importance in solving complex mathematical problems.

Conformal Blocks: Understanding Young Diagrams and Weight States