01:41

Poncelet triangles about the incircle, containing an equilateral: loci of several triangle centers.

01:58

Circle-inscribed Poncelet triangles with an equilateral: locus of the vertex of the Kiepert parabola

01:16

Circle-inscribed Poncelet triangles with an equilateral: stationary X(110)

04:36

Circle-inscribed Poncelet triangles w/ an equilateral III: the locus of the inconic centers

05:32

Circle-inscribed Poncelet with an equilateral II: the double stationarity of X74, X110

06:23

Circle-inscribed Poncelet triangles with an equilateral I: the X(3)X(74) axis is stationary

02:43

Poncelet triangles between two ellipses: properties of the locus of the orthocenter X(4)

01:47

Poncelet Triangles with Circular Caustic: The loci of X2, X4, and X7.

01:26

Four special Poncelet triangle families (circular caustic): focal-X1, iso-X2, focal-X4, and focal-X7

02:13

Poncelet Triangles with Circular Caustic: The loci of X3, X5, and X8.

05:56

MacBeath Poncelet family: vertex and area centroids are stationary; perimeter one sweeps ellipse

03:33

Three Poncelet triangle families with stationary orthocenter X(4)

05:38

Poncelet triangles with fixed barycenter: choosing the caustic

05:53

Poncelet Polar-to-Harmonic Polygons: sum of tangents of half angles is conserved

06:49

Poncelet triangles w/ circular caustic X: a family with fixed barycenter and Nagel line

02:10

Bicentric Poncelet N=5: polar polygons conserve the sum of half-angle sines

02:59

Poncelet triangles w/ circular caustic IX: the "orthofocal" circumellipse, loci and an invariant

03:27

Poncelet triangles w/ circular caustic VIII: inverse-in-incircle of circumcircle

05:40

Isocurves of area for envelope of ellipse bisectors III: circular domain

12:41

Isocurves of area for envelope of ellipse bisectors II: more cases, self-intersections, etc.

04:01

Isocurves of area for envelope of ellipse bisectors I: Q1 is a focus

02:07

MacBeath Poncelet N=3: Inversive image of sidelines wrt circumcircle conserves sum of 1/(ri^2)

04:51

Inversive image of Bicentric Polygons II: N=5 conserves perimeter (sum of arclengths)

05:05

Inversive image of Bicentric Polygons I: sum of arclengths (perimeter) is conserved

01:56

Poncelet triangles w/ circular caustic VII: foci of X(3) locus dependence on C

06:50

Poncelet triangles w/ circular caustic VI: nifty circular locus of X(36)

06:08

Poncelet triangles w/ circular caustic V: honey, I shrunk the triangle centers!

05:36

Poncelet triangles w/ circular caustic IV: amazing foci of the circumcenter locus

04:46

Poncelet triangles w/ circular caustic III: the loci of X2,X3,X4,X5

12:31

Poncelet triangles w/ circular caustic II: loci of centers over caustic centers

03:07

Poncelet triangles w/ circular caustic I: level curves of caustic radius

01:27

MacBeath Poncelet Family (even N): diagonals meet at a point

03:25

MacBeath Poncelet N=4: sidelengths vs. Poncelet parameter

03:45

Poncelet MacBeath N=3 Conservations and Spherical Curve of the Sidelengths

02:40

Conservations of "MacBeath" Poncelet Polygons: sum of squared sidelengths and double-angle cosines

04:19

Conjecture for the locus of X1 (incenter) over Poncelet triangles: a conic iff the pair is confocal

02:32

Conservations of MacBeath Poncelet triangles vs. the confocal (elliptic billiard) family.

05:55

Locus Invariants of Circle-Inscribed Poncelet Triangles IX: X2 and X4 and the outer projected conic

05:22

Locus Invariants of Projected Poncelet Bicentric Polygons VIII: vertex and area centroids

05:10

Locus Invariants of Projected Circle-Inscribed Triangle Families VII: over all nested caustics

06:01

Locus Invariants of Projected Poncelet Triangles VI: sliding bicentric caustic

07:24

Locus invariants of projected Poncelet triangles V: rotate outer conic about circular caustic: bad!

06:40

Locus invariants of projected Poncelet triangles IV: rotating concentric and MacBeath inellipses

08:06

Locus invariants of projected Poncelet triangles III: rigid rotations of generic caustic

03:36

Locus invariants of projected Poncelet triangles II: rotating Chapple's circular caustic

16:25

Locus invariants of projected Poncelet triangles I: Chapple's porism w/ a rotating caustic

02:34

Strophoids IV: a hidden equilateral

05:23

Beautiful MacBeath Poncelet N=5 (II), caustic a semi-confocal hyperbola, 5 concyclic points

13:55

Strophoids III: locus of the foci of inconics to a complete quadrilateral

07:06

Strophoids II: a special strophoid triad associated with a triangle and its intouch triangle

09:49

Strophoids I: construction, finding the focus

13:39

Beautiful MacBeath Poncelet N=5 (I): diagonals meet on a circle of 5 points

04:19

Poncelet n=4 between two identical unit circles

04:04

[see proof] Permutation Ellipse VI: Circumellipse area invariant under center permutations

06:15

Permutation Ellipses V: The Self-Permuting Sextic

11:37

Permutation Ellipses IV: Equal Area Circumellipses and a Sextic Locus

08:19

[see challenge] Permutation Ellipses III: P on the Steiner Circumellipse and Homothetic Poncelet

06:54

Permutation Ellipses II: doubling up, quintuple tangencies, straight loci (read note)

05:41

Permutation Ellipses I: locus of permutations over P on circumcircle

14:53

ICGG2022 [full]: "The Wrought-Iron Beauty of Poncelet Loci"