What Are Projective Transformations?

Explanations 3

• We define a pencil as the set of all lines through a point, and we define a range as the set of all points on a line. When we draw these two geometric objects together, we see a…

  By Tae Hyung Kim, Alex Federspiel

• The Cross Ratio Given four collinear points AAA, BBB, XXX, YYY we define their cross ratio to be (A,B;X,Y)=XAXB:YAYB.(A,B;X,Y) = \frac{XA}{XB} : \frac{YA}{YB}.(A,B;X,Y)=XBXA​:YB…

  By Evan Chen, Expii Team

• In the figure below, let's prove using projective transformations that (T,D;B,C)=−1(T,D;B,C) = -1(T,D;B,C)=−1. (It's also possible to produce a proof using Ceva and Menelaus.) F…

  By Evan Chen