Eclectic Illuminism: Applications of Affine Geometry

Glesser, Adam; Rathbun, Matt; Serrano, Isabel M.; Suceavă, Bogdan D.

doi:10.1080/07468342.2019.1565588

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…This property is directly related to invariants in the plane under the action of the Möbius group in the plane. Therefore, by studying properties related to cycles we are actually investigating invariant properties, as stated by Felix Klein's 1872 Erlangen Program (for a recent discussion of the relevance of this connection, see [7]). A thorough investigation of cyclicity is by no means an effort focused on particular cases, and a display of methods useful to understand it reaches deep into the very structure of the foundations of geometry.…”

Section: Discussionmentioning

confidence: 99%

Power of a point: from Jakob Steiner to modern applications

Gîrban

Suceavă

2022

Math. Gaz.

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"What should we use?" seems to be the question when one approaches a plane geometry problem. In many ways, Euclidean geometry is a laboratory in the realm of logic, an ideal place where one can see how alternative methods can be employed to solve problems. What detail might represent a hint? And from among many choices, what method could one consider? Does the geometric structure suggest a certain type of approach?

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Section: Discussionmentioning

confidence: 99%

Power of a point: from Jakob Steiner to modern applications

Gîrban

Suceavă

2022

Math. Gaz.

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“…There are profound nuances related to this approach, all connected to Felix Klein's Erlangen Program (see e.g. [6]).…”

Section: Does the Nine-point Circle Theorem Have Any Direct Elementarmentioning

confidence: 99%

The fruit of the meditations of a young Lieutenant of the Engineers: A Theorem of Major Impact and Its Applications. Two Centuries from the Discovery of the Nine-Point Circle

Suceavă

2021

CMI

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The Nine-Point Circle Theorem was first obtained in a joint work written by C.-J. Brianchon and J.-V. Poncelet. Since the authors of this Theorem presented it in their original work as a principle in geometry, we are invited to reflect whether there are some direct applications of this Theorem in advanced Euclidean geometry. Our exploration only confirms the original authors’ foretelling intuition, since un nouveau principe à la géométrie élémentaire is expected to admit applications. We regard the Nine-Point Circle Theorem in the overall context of the history of ideas and, pursuing Philip Davis’ thoughts, we regard the geometry of triangle as a chapter in the history of mathematical cultures.

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Ptolemy Through the Centuries

Ibragimov

Suceavă

2023

Mathematics Magazine

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Eclectic Illuminism: Applications of Affine Geometry

Cited by 3 publications

References 7 publications

Power of a point: from Jakob Steiner to modern applications

Power of a point: from Jakob Steiner to modern applications

The fruit of the meditations of a young Lieutenant of the Engineers: A Theorem of Major Impact and Its Applications. Two Centuries from the Discovery of the Nine-Point Circle

Ptolemy Through the Centuries

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