Geometry

The Five Squarable Lunes
Constructing the Heptadecagon
Generalizing Pythagoras and Carnot
Iterative Isoscelizing
Parabola Through Four Points
Euclid's Proposition III,20 and its Converse
Sphere Packing In Curved Space
Pascal's Mystic Hexagram
Min-Energy Configurations of Electrons On A Sphere
Generating Functions for Point Set Distances
Curvature of Linear Interpolation
An Optical Illusion
Platonic Solids and Plato's Theory of Everything
Euclid's Plan and Proposition 6
Volume of n-Spheres and the Gamma Function
Ptolemy's Orbit
Spiral Tilings and Integer Sequences
Apollonius' Tangency Problem
Loci of Equi-angular Points
Heron's Formula and Brahmagupta's Generalization
Heron's Formula for Tetrahedra
The Orbit of Triangles
Perpendicular Regression Of A Line
Rolling Spheres and Cones
Cramer's Paradox
The Lemniscate and Spacetime
A Swiss Triangle
The Longest Night
Factoring Convex Figures
Smallest Quadrilateral With Distinct Integer Sides
Mean Distance from Vertex to Interior of Plane Figures
The Mystery of the Grazing Goat
Triangles in a Row
Old Notes on Curvature
Did Archimedes Know Gauss-Bonnet?
Pent Up Ratios
Thinking Outside the Triangle
Napoleon's Theorem
Curved Paths and Linear Segments
On the Ellipse
The Shape of Coincidence
Double Equations from Triangles in Squares
Equidistant Curves
Distances In Bounded Regions
Cyclic Quadrilaterals Revisited
Embedding Non-Euclidean Within Euclidean Geometry
Forests or Trees on a Complex Plain
Acute Problem
On de Bruijn Grids and Tilings
Areas of Conic Quadrilaterals
 Archimedes on Spheres and Cylinders
Pappus' Theorem
Quintisecting an Angle
Quadrilateral In a Circle
Volume Under a Triangle
Constructible Points and Coverable Points
A Quarky Formula for Volume of Parallelpiped
Piero della Francesca's Tetrahedron Formula
Automedian Triangles
Piano Keys
On Ptolmey's Theorem
N-Fold Polygonal Spirals
Equal Bisectors and Isosceles Triangles
Equation of a Triangle
Highly Heronian Ellipses
No Equilateral Triangles on a Chess Board
Net Area and Green's Theorem
Ringing of the Changes (The Shape of 4!)
Partitioning Polygons
The Resultant and Bezout's Theorem
Stochastic Rhombic Tiling
Triangle in a Square
Diophantine Geodesic Boxes
Angular Angst
Triangular Tilings of a Sphere
Zeno's Mice and the Logarithmic Spiral
Path Lengths and Coordinates
The Cube Unfolded
Areas of Triangle Partitions
Revisiting the Four-Point Parabola
Conformal Coordinates
Morley's Trisection Theorem
Bisecting Plane Figures
Isospectral Point Sets in Higher Dimensions
Hyperbolic Motion and Parabolic Chords
Exponential Spiral Tilings
Harmonia Mensurarum
Constant Headings and Rhumb Lines
Enveloping Circular Arcs
Normals From A Point To An Ellipse
Cutting Self-Similar Pentagons
The Tetratorus and Other Multi-Layered Polyhedra
The Curvatures of Hypersurfaces
Menelaus and Ceva
Carnot, Organizer of Transversals
Non-Periodic Tilings With N-fold Symmetry
Intersecting Circles
Aperiodic Tilings
Tilings Based on Perrin's Sequence
Routh's Formula by Cross Products
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