Projective Morphology 15:  The Imaginary
Channel: Daniel Hafner
Date: 24/05/2021

CORRECTION:  18:26 The hyperboloid is partially flattened only if the ellipsoid is partially flattened.

We can now broaden our awareness of what a point is, and what a line is, not to mention a plane, or a curve.  For the familiar sedentary variety, “visible” seems a more objective term than “real,” since imaginary elements are just as real.  Unlike their bourgeois counterparts, they are in cyclical movement.

Familiarity with harmonic conjugates, pole and polar, involution, and Steiner circles is presupposed.

As mentioned last time, hyperbolic and elliptic involution shall be called breathing and circling involution, respectively.

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:  imaginary points, imaginary lines, imaginary conics, amplitude, density, Apollonian circles, projective geometry, synthetic geometry, evolution of consciousness, Karl von Staudt, Rafael Bombelli