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**Constructions on the Lemniscate**

The Lemniscatic Function and Abel’s Theorem

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What is the lemniscate?

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What is the lemniscate?

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**Who studied the lemniscate?**

Niels Abel Jacob Bernoulli Ferdinand Eisenstein Leonhard Euler Carl Gauss

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Arc Length

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Arc Length

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Arc Length

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Arc Length

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**The Lemniscatic Function**

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**The Lemniscatic Function**

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**The Lemniscatic Function**

The Sine Function The Lemniscatic Function

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**The Lemniscatic Function**

Basic Identities The Sine Function The Lemniscatic Function

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Basic Identities

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Basic Identities

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**The Lemniscatic Function**

The Addition Law The Sine Function The Lemniscatic Function

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The Addition Law

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**Multiplication by Integers**

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**Multiplication by Integers**

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**Multiplication by Integers**

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**Multiplication by Integers**

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Constructions

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Constructions

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Constructions

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Constructions

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Abel’s Theorem

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Abel’s Theorem

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Abel’s Theorem

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Abel’s Theorem

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Abel’s Theorem

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Abel’s Theorem

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Abel’s Theorem

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

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