Attractive Centers (4 papers)
Four papers on invariant attractive centers, chests and hearts, symmetry-displacement geometry, radial response, and analytic triangle-center constructions.
Ismaa3iil
Mathematical and physical investigations.
Attractive Centers
Other papers
Power Centers and Hull-Power Centers
Drag the vertices of a triangle or tetrahedron and compare vertex power centers with uniform-solid hull-power centers. Explore p = 1.01 to 24.99 for triangles or 4 − 2√2 to 19.95 for tetrahedra. Overlay nearby ETC centers, inspect their independent attractivity certificates, and export the curves. Research and authorship by Ismail Hammoudeh, with extensive use of ChatGPT acknowledged.
Triangle Centers Inspired by Physics
Explore physical laws and measurement protocols that select natural points of a triangle through a 274-page research monograph, a free 66-entry geometry explorer, the updated atlas, lecture notes, and 102 editable PowerPoint slides.
Tetrahedral Families (4 papers)
Four papers on power families, face constraints, Euler projection, and skeletal-centroid projection in tetrahedral geometry.
Dihedral-Angle Sums in Orthocentric, Power-k, and Isodynamic Tetrahedra
A publication-oriented study of dihedral-angle sums, rigorous ranges for several tetrahedral families, and explicitly labelled open conjectures.
Plane Sections of Symmetric Tetrahedral Cones
Inverse fibers, Poncelet 3-porisms, phase transitions, and triangle loci in a one-parameter family of symmetric trihedral cones.
Reciprocal Periods and Primality
A period-primality toolbox and an investigation of the rarity of small-index pseudoprimes.
Supercenter–Soddy Project (2 papers)
Two companion papers on the in-excentral supercenter, equal-detour points, and Soddy–orthocenter specializations.
The Triangle Sky (2 papers)
A two-paper project on triangle centers lifted to tetrahedral apices, triangle stars, hyperstars, and the reproduction of ETC centers.
Beauty of Triangle Centers
Explore and rank fractal attractors in the barycentric space of triangles through equal-position comparisons of neural interestingness, raw quadtree compressibility, and modified compressibility, with two complete downloadable atlases.
Triangle Centers Relative to Their Cevian, Circumcevian, and Pedal Triangles
An algebraic and computational study of how triangle centers are reclassified when the reference triangle is replaced by a cevian, circumcevian, or pedal triangle.
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