If you have a garden of rocks, it is possible that no rock has the same weight as the average. ~Carl Jung

Conjectures

Our hands have many degrees of freedom, nodal and distributed.

I am doing research into how we can use our hands like an abacus.


Addition, Subtraction, Multiplication and Division Practice


Generalization of the Pigeonhole Principle

Theoretical Physics of Spring

Hyper Tetrahedron Invariants

Honeycomb Trigonometry

Fuel Loop Problem Proof Sketch (with extension to applied problem)


Research Programs (see Imre Lakatos)

Geometric Connection Theory


Statistics

Loss Functions Seminar

Loss Functions Seminar 2 (showing maximum likelihood estimate is optimal given large number of samples)

There is a common misconception that data typically is normally distributed.

Analysis of Coincidence

Quantification Problem 1

Quantification Problem 2 with Safety Applications

Multiple Sensor Averaging can Reduce Error

(As a note, sometimes too much input to an algorithm can make a problem harder to solve. For example, if too many people in a car are giving the driver instructions, that can make driving more difficult.)

Exponential Linear Region (for quick risk calculations given pressure)


Number Theory

arithmetic hacks

Real Number Subtraction Theorem

Rational Number Theorem

Induction with Examples

Multiplicative Commutativity (inductive proof and non axiomatic proof)

Euclid's Division Lemma

Exponentiation Lesson

Basis Representation Theorem

Basis Representation Theorem optional material

Quantifier Chains

Largest Public Prime Number code reference