Explore how physical experiments select a triangle’s centers, with a complete research monograph, an interactive geometry lab, a research atlas, and undergraduate teaching materials.
The complete monograph brings the six physical studies together with a common introductory chapter, six thematic appendices, 159 images, a 66-entry center and evidence index, and 32 consolidated references.
The source and evidence ZIP contains the editable LaTeX manuscript and figures, selected computational records, editorial audits, and an integrity manifest.
Drag the triangle’s vertices and compare 66 physical selectors with classical centers. Read the theory and evidence behind each point, or compare seven shape-fingerprint diagrams with optional ETC neighbors.
Most physical-center locations use the research atlas’s interpolation; the app identifies its direct solvers, exact aliases, and unavailable cases. The methods guide explains the evidence and numerical limits.
A self-contained introduction to balance, charges and currents, membranes and fluids, quantum and random motion, heat and reaction, and optics. Includes 32 vector figures and 83 questions and exercises with answers.
The companion ZIP contains the complete LaTeX source, offline interactive demonstrations, coverage records, and selected evidence files.
Six lectures and an optional appendix covering balance, fields, elasticity, quantum and random motion, diffusion and reaction, and optics.
The revised presentation includes editable mathematical equations, correctly formatted subscripts and superscripts, clearer graph legends, and improved figure annotations. Speaker notes, chart data, and animation sequences are included.
Physical laws and measurement protocols select points through equilibria, maxima, probability means, and singular limits. The manuscript organizes quantum, conformal, electrostatic, magnetic, thermal, fluid, mechanical, reaction, and optical constructions, including parameter families and exact classical reductions.
Accessible derivations are followed by numerical methods, individual contour atlases, Encyclopedia of Triangle Centers location comparisons, shape fingerprints, and vertex-motion attractivity evidence.
Start with the classical realizations, then follow the result sheets through increasingly specialized physical selectors.
Centroid, incenter, Spieker center, symmedian point, circumcenter, orthocenter, nine-point center, and Fermat center.
Ground and excited-state selectors, thermal quantum means, and classical billiard fluctuations.
Diffusion, electrostatics, conducting plates, skeleton charge centroids, and a magnetic-field minimum.
Poisson models, survival, fluid torsion, heat maxima, nonlinear membranes, and density means.
Gravity-loaded plates, buckling modes, compliance, thermal variance, and bending-energy centroids.
Production-removal, logistic population, darkness, fluorescence, inverse-square illumination, and solid angle.
Additional vertex, surface, and volume-current selectors M2–M7, prism Robin centers L3–L4, and updated electrostatic and magnetic attractivity evidence.
The 30 September 2026 atlas extends the original 58 entries to 66 with M2–M7 and L3–L4. It provides definitions, derivations, contour atlases, ETC comparisons, and revised electrostatic and magnetic attractivity evidence.
Some constructions have no convenient closed form; the atlas makes no blanket transcendence or ETC nonmembership assertion. Uniqueness, branch conventions, dimensions, and limiting procedures remain part of each model.
The atlas is prepared from the project’s draft and computational studies. Its title page leaves authorship and submission metadata unassigned. The lecture notes and explorer carry their own dated evidence and methods guidance.
Triangle Centers Inspired by Physics · Consolidated research edition · 3 October 2026