Philosophy of Proofs

Two unobvious yet trivial proofs.

Correctness of Fast Fourier Transform

Topology scraps

Besikovitch’s problem

Riemann programs

Tiling Constant Curvature Spaces with the Right Regular Pentagon, coordinates

Phone Cell Patterns

Tangents and Curvature

Bézier curves

The Affine Connection

The meaning of R

Symplectic Manifolds

Manifold in a Box

Isometries

Projective Geometry fragments

Elementary Geometry on a Complex

Computing the Boundary of a Complex

Boundary Conditions for PDEs.

Barycentric coordinates

The Platonic Polytope (applet)

Area of Intersection of Polygons

Sliced Polytopes

Conventional Sphere Packing

The Simplex and its Angles

Angles between sub-spaces—Grassman stuff

Icosahedron & Dodecahedron

Topological link and induced current

Turing’s Knots

My take on formal systems; A Tiny bit of Model Theory

An axiomatic introduction to abstract vector spaces

Linear Transformations on vector spaces

Linear Differential Equations

Algebras over vector spaces, associative and not

Hilbert Space

There are c continuous functions and c points in Hilbert space.

Implicit Methods

Implicit Mesh Code, Sparse linear solutions

The Alias Alibi distinction

Content of the n dimensional ball

Volume of some Compact Lie Groups

Generating random orthogonal matrices

Axioms for Groups

Code for Fields in a computer, matrix inversion.

Special Matrices and their Spectrum

Unimodular Matrices

Code for eigenvalues and eigenvectors.

Elementary questions about integration on the complex plane.

Experimental Quaternions and Octonions and general division algebras

Computational Clifford Algebras and Hypercomplex numbers

Polynomial Roots

Incomplete Multivariate polynomials

Rank and reduced row echelon form

Rational Gram Schmidt, Orthogonal sub-spaces and intersection of sub-spaces

Code for determinants (C, OCaml, Algol68)

A numerical coincidence?

A glimpse at p-adic numbers

Order Types

Dedekind cuts of partial orderings

Stowaways

See Math Connection in here

Type equivalence, Infinite trees, Anti Foundation set theory

Axioms for Sets, Intersections of Sets of Sets

Completeness of Predicate Calculus

Note on minimal coverings

A Functional Equation

Constructing a Brownian Function

Applied Lambda Calculus

A general recursive function

Some Bayesian statistics and Likelihood note.

Factoring with the Quadratic Sieve

Finding Primes

Counting constrained bit arrays

Stationary Boolean Patterns

Logical quantification

Critical Density of Links

Covariant and Contravariant; Tensors and Types

Variables

Computing π; Computing e; π & e in various radixes

Distribution of continued fraction terms

Correlation is not transitive.

Summing a slowly convergent series

Finding foci of an ellipse

ellipse

Elliptic Curve

The Ergodic(?) Folium

Dividing an irregular Pizza

Cycloid

Simple trigonometry proof

bent beams[with pictures, with Runga-Kutta precision]

Decoding obscure symbols.

Symbols that I use

Equality or not

Compressive Sensing

Miscellany

Relations and Graphs

Arithmetic coding, set display, etc.

Notions of Patterns

New Foundations (HoTT)

Formulae in html context

External Math and Physics Pointers

Kinetic energy

19th century origins of stress-energy tensor

Banach Area & Crystals

Bug in Banach Crystals Idea

Floating Cube

Cube’s gravity,
Spinning Blob

Efficient Hydraulics

Lab Electricity Delta Puzzle

Wooden Puzzles

Gravitational Assembly Energy

Accretion Rings

Cold Neutrinos as Dark Matter

Down on Inflation

Solution to Potential using ∞ virtual Charges

The Structure of Diamond
and ice

Maxwell’s Light

Probability Nexus

Lambertian Reflection

Whiteout

Vortices

Notes on Tegmark’s TOE

1D Hydro Dynamics Code (shock wave)

2D minimalistic Isothermal Hydro

3D Elasto Dynamics Code

Cauchy momentum equation

Landau’s superfluid notion

Idea for ultra high resolution radio
interferometry

Six Axis Stress Gauge
and Virtual touchy-feely

Plucked String (Fourier Series)

Fourier Transform of image

Tumbling rigid body and general moments

Physical Libration

The Lagrange Points

Lagrange Interpolation

Close Encounters (orbits, three body)

Yet another Digital Orrery

New Planet?

compound pendulum using Lagrangian logic

Short note on the Hamiltonian

Fizzy Drinks

time

Devising a time signal

Time dilation in Gravity Well

Quantum Computers

Gaussian quantum particle

Einstein Podolski Rosen Paradox

A bit of QED

SU(3) and quarks

circular polarization

Notes on Particle Spin

Ions

Action

Edge of Chaos and Economics

Understanding

Things are as they are because they were as they were.

Logic, Evolution, Math etc.

Connection between logic and λ calculus

Nested Sets

ext