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a super nice functional equation

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the geometry of the third derivative

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Integrating the impossible

Michael PennMay 26, 2024

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my new favorite proof of this classic result

Michael PennApr 2, 2024

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$journey into fractals: the Cantor set and ternary expansion.$

journey into fractals: the Cantor set and ternary expansion.

Michael PennNov 24, 2023

Why are there no 3 dimensional "complex numbers"?

Michael PennNov 23, 2023

The craziest definition of the derivative you have ever seen!

Michael PennNov 1, 2023

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the equation Ramanujan couldn't solve!!

Michael PennOct 6, 2023

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a formula for the "circumference" of an ellipse.

Michael PennOct 2, 2023

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Climbing past the complex numbers.

Michael PennSep 22, 2023

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what is the Gateaux derivative?

Michael PennJul 29, 2023

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Deriving Euler's formula four ways!

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a surprisingly interesting sum -- 2 ways!

Michael PennJul 3, 2023

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Euler's other constant

Michael PennJun 19, 2023

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A unique approach to the half-derivative.

Michael PennJun 18, 2023

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a quaternion version of Euler's formula

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The universal enveloping algebra

Michael PennDec 2, 2022

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One of the most important algebras -- The Witt Algebra

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The strange cousin of the complex numbers -- the dual numbers.

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Real Analysis | A convergent sequence is bounded.

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Featured Results

why only some infinite power towers are well defined.

the best proof that the real numbers are uncountable!!

can you evaluate this sum??

a super nice functional equation

the geometry of the third derivative

The unreasonable effectiveness of linear algebra.

I can solve any quintic equation!!

this defines my favorite function

Integrating the impossible

my new favorite proof of this classic result

journey into fractals: the Cantor set and ternary expansion.

Why are there no 3 dimensional "complex numbers"?

The craziest definition of the derivative you have ever seen!

the equation Ramanujan couldn't solve!!

a formula for the "circumference" of an ellipse.

Climbing past the complex numbers.

what is the Gateaux derivative?

Deriving Euler's formula four ways!

a surprisingly interesting sum -- 2 ways!

Euler's other constant

A unique approach to the half-derivative.

a quaternion version of Euler's formula

The universal enveloping algebra

One of the most important algebras -- The Witt Algebra

The strange cousin of the complex numbers -- the dual numbers.

Real Analysis | A convergent sequence is bounded.

Featured Results

why only some infinite power towers are well defined.

the best proof that the real numbers are uncountable!!

can you evaluate this sum??

a super nice functional equation

the geometry of the third derivative

The unreasonable effectiveness of linear algebra.

I can solve any quintic equation!!

this defines my favorite function

Integrating the impossible

my new favorite proof of this classic result

journey into fractals: the Cantor set and ternary expansion.

Why are there no 3 dimensional "complex numbers"?

The craziest definition of the derivative you have ever seen!

the equation Ramanujan couldn't solve!!

a formula for the "circumference" of an ellipse.

Climbing past the complex numbers.

what is the Gateaux derivative?

Deriving Euler's formula four ways!

a surprisingly interesting sum -- 2 ways!

Euler's other constant

A unique approach to the half-derivative.

a quaternion version of Euler's formula

The universal enveloping algebra

One of the most important algebras -- The Witt Algebra

The strange cousin of the complex numbers -- the dual numbers.

Real Analysis | A convergent sequence is bounded.

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