Projective Geometry: Historical Overview

In course

Description

This lecture provides an overview of the historical development of projective geometry, focusing on key figures such as Alberti and Piero della Francesca. It explores how these mathematicians contributed to the understanding of perspective and distance points, shedding light on their innovative approaches and the impact of their work.

Instructor

Official source

https://mediaspace.epfl.ch/media/0_fn6riy15

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (54)

Piero della Francesca

Piero della Francesca (ˌpjɛəroʊ_ˌdɛlə_frænˈtʃɛskə, USalso-_frɑːnˈ-, ˈpjɛːro della franˈtʃeska; ; 1415 – 12 October 1492) was an Italian painter of the Early Renaissance. To contemporaries he was also known as a mathematician and geometer. Nowadays Piero della Francesca is chiefly appreciated for his art. His painting is characterized by its serene humanism, its use of geometric forms and perspective. His most famous work is the cycle of frescoes The History of the True Cross in the church of San Francesco in the Tuscan town of Arezzo.

Distance

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network).

Great-circle distance

The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines. In spaces with curvature, straight lines are replaced by geodesics.

Geographical distance

Geographical distance or geodetic distance is the distance measured along the surface of the earth. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic problem. Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an exact distance, which is unattainable if one attempted to account for every irregularity in the surface of the earth.

Correlation (projective geometry)

In projective geometry, a correlation is a transformation of a d-dimensional projective space that maps subspaces of dimension k to subspaces of dimension d − k − 1, reversing inclusion and preserving incidence. Correlations are also called reciprocities or reciprocal transformations. In the real projective plane, points and lines are dual to each other. As expressed by Coxeter, A correlation is a point-to-line and a line-to-point transformation that preserves the relation of incidence in accordance with the principle of duality.