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Concyclic Harmony: Exploring Mikkel’s Pentagram Theorem episode artwork

EPISODE · Jul 30, 2025 · 5 MIN

Concyclic Harmony: Exploring Mikkel’s Pentagram Theorem

from Intellectually Curious · host Mike Breault

In this episode, we dive into Mikkel’s Pentagram Theorem: five circles arranged around a pentagram intersect such that the adjacent circles meet at a pentagram vertex, and the second intersection points all lie on one circle. We show how two starting viewpoints—from a pentagon extended into a star, or from circumcircles around the star’s tips—lead to the same elegant structure. We also discuss the converse: if the five circle centers are concyclic, the connecting lines of those second intersections form a new pentagram whose vertices sit on the original circles. Plus a touch of history and a visual intuition to glimpse the hidden order in geometry.Note:  This podcast was AI-generated, and sometimes AI can make mistakes.  Please double-check any critical information.Sponsored by Embersilk LLC

Episode metadata supplied by the publisher feed · Published Jul 30, 2025

What this episode covers

In this episode, we dive into Mikkel’s Pentagram Theorem: five circles arranged around a pentagram intersect such that the adjacent circles meet at a pentagram vertex, and the second intersection points all lie on one circle. We show how two starting viewpoints—from a pentagon extended into a star, or from circumcircles around the star’s tips—lead to the same elegant structure. We also discuss the converse: if the five circle centers are concyclic, the connecting lines of those second interse...

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This episode is 5 minutes long.

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This episode was published on July 30, 2025.

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In this episode, we dive into Mikkel’s Pentagram Theorem: five circles arranged around a pentagram intersect such that the adjacent circles meet at a pentagram vertex, and the second intersection points all lie on one circle. We show how two...

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