# Constructions on the Lemniscate

## Presentation on theme: "Constructions on the Lemniscate"— Presentation transcript:

Constructions on the Lemniscate
The Lemniscatic Function and Abel’s Theorem

What is the lemniscate?

What is the lemniscate?

Who studied the lemniscate?
Niels Abel Jacob Bernoulli Ferdinand Eisenstein Leonhard Euler Carl Gauss

Arc Length

Arc Length

Arc Length

Arc Length

The Lemniscatic Function

The Lemniscatic Function

The Lemniscatic Function
The Sine Function The Lemniscatic Function

The Lemniscatic Function
Basic Identities The Sine Function The Lemniscatic Function

Basic Identities

Basic Identities

The Lemniscatic Function
The Addition Law The Sine Function The Lemniscatic Function

Multiplication by Integers

Multiplication by Integers

Multiplication by Integers

Multiplication by Integers

Constructions

Constructions

Constructions

Constructions

Abel’s Theorem

Abel’s Theorem

Abel’s Theorem

Abel’s Theorem

Abel’s Theorem

Abel’s Theorem

Abel’s Theorem

The End Thank you for coming! Special thanks to Dr. Hagedorn for his many valuable insights