Geometrikon is a gallery of Topics in Geometry and geometric subjects from other fields. It started as a list of examples from Geometry, Euclidean, Affine, and Projective, and evolved for some time to contain proofs and discussions on various topics.
The subjects listed below are continuously reviewed and updated with the intention to make the exposition as complete as possible and give enough references to related subjects and bibliography.
Originally the gallery included several hundreds of topics, some rudimentary and intentional for future discussions, some informal, some included for aesthetic reasons, some in the form of detailed expositions with proofs.
Presently the old html-files of the gallery, representing the topics, are gradually replaced with pdf-files and updated contents. The aim for this is a stronger coherence in the presentation of material and a better quality of figures. To achieve this, the presentation of the topics is organized as a collection of possibly independent pdf-files.
The topics below are listed alphabetically using some relevant for their content word of the title. To search quickly Geometrikon for an item of your interest, display the "search box" by pressing the key-combination CTRL+F, write there the search word and press the OK button or the ENTER-key.
The "hyper-references" in the new versions with pdf-files, which refer to other pdf-fils are "relative" and work properly in "firefox" if you read them on-site. They work correctly off-site, if you download the respective files and put them all in the same folder.
If you like to be informed on updates and new links to pdf-files of this gallery, send me an email to add you in the list of updated-urls-recipients.
- Abridged notation [New pdf-version] 01/09/2009, 28/11/2018 , 10/12/21Contents: 1 Introduction , 2 Abridged notation, cartesian coordinates, homogenization , 3 Pencils of conicss , 4 Interpretation of the members of a pencil , 5 Bitangent conics and pencils , 6 Abridged notation, line formularium , 7 Abridged notation, conics formularium , 8 Cross ratio on the conic , 9 The Chasles-Steiner definition of a conic , 10 Some applications, Pascal’s theorem , 11 Maclaurin’s conic generation method , 12 Double tangency of two conics , 13 Polygons inscribed and circumscribed about conics .Related topics : Cross Ratio, Homographic relation, Projective line. Projective plane. The quadratic equation in the plane.
- Affine transformations of the plane (Affinities) [New pdf-version] 01/09/2009, 14/05/2019Contents: 1 Definition and group property, 2 Determination of an affinity, 3 Additional fundamental properties of affinities, 4 Special kinds of affinities, 5 Axial affinities or homologies, shears, strains, 6 Affinities leaving invariant a triangle, 7 The period of an affinity, 8 Translations, 9 Dilatations, 10 Shears, 11 Strains, 12 Invariant pencils, 13 Equiaffinities as products of reflections, 14 Conjugacy for affinities with fixed points, 15 Elliptic affinities, 16 Orbits of points under equiaffinities, 17 Classification of equiaffinities, 18 Analytic description of orbits of equiaffinities, 19 Remarks and exercises on orbits of equiaffinities, 20 Affine equivalence of conics, 21 Affinities preserving a non-degenerate conic.
- Illustration of the curve "Witch of Agnesi" and description of its generation.
- A locus generated by some algebraic operations on (complex) points.
- All Conics Circumscribed created : 27/10/2007, updated : 27/08/2009 eucDetermination of the family of all conics circumscribing a triangle and tangent to a line.
- As before but now the line separating the three vertices of the triangle.
- A study of the conics circumscribed about a triangle.
- Determination of the family of all parabolas circumscribing a triangle. Some remarks on the two parabolas through four points.
- A property of lines defined through ratios on the sides of an angle.
- Defining a line through certain length-ratios on the sides of an angle.
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