Projective Morphology 13:  Inversion
Channel: Daniel Hafner
Date: 2021-03-05

The customary point-to-point reflection at a circle is not the only way to invert, nor even the most consistent.

Try pausing and picturing the transformations on your own, or even constructing them.

Presupposes familiarity with polarity (usually known as duality), introduced in the first installment of this series, and with poles and polars, introduced in the twelfth.

This presentation is part of a series:
     1 Polarity  https://youtu.be/1xcRJdxgKuU
     2 The Infinitely Distant  https://youtu.be/nlKTRYDBi1Q
     3 Metamorphosis  https://youtu.be/mW705pKwUvo
     4 Desargues's Triangle Theorem  https://youtu.be/S9uJbCtc1IM
     5 Harmonic Conjugates  https://youtu.be/9dSysBCjMtQ
     6 The Fundamental Harmonic Figure  https://youtu.be/xM__3Rv21BY
     7 Perspective and Projection  https://youtu.be/exly1JXIGSM
     Interlude  https://youtu.be/Us3Hj_CBhBU
     8 Curves of the Second Order  https://youtu.be/gMvsutuNTGg
     9 Proof of Steiner  https://youtu.be/g5CocUQwdbc
     10 Conic Sections  https://youtu.be/m-3Dt-NDMQ0
     11 The Theorems of Pascal and Brianchon  https://youtu.be/Y8mf3gP5tCg
     12 Pole and Polar  https://youtu.be/6DN5ahPHG_Y
     13 Inversion  https://youtu.be/YueFf2XFmXE
     14 Progression and Involution  https://youtu.be/gEJsKXVM0Bk
     15 The Imaginary  https://youtu.be/paKMtN0c6bw
     16 Counterspace  https://youtu.be/hY0ETd75IjM
     The Human Skeleton  https://youtu.be/JzLMQVCjg24

Other topics:  circle inversion, counter-pole, counter-polar, visualization exercises, lemniscate, folium, cubic, quartic, Platonic solids, projective geometry, Apollonius of Perga, Jacob Bernoulli, Descartes, Carl Kemper, Cassini, Olive Whicher