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THE LEMNISCATIC FUNCTION AND ABEL’S THEOREM Constructions on the Lemniscate.

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Presentation on theme: "THE LEMNISCATIC FUNCTION AND ABEL’S THEOREM Constructions on the Lemniscate."— Presentation transcript:

1 THE LEMNISCATIC FUNCTION AND ABEL’S THEOREM Constructions on the Lemniscate

2 What is the lemniscate?

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

5 Arc Length

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9 The Lemniscatic Function

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11 The Sine Function The Lemniscatic Function

12 The Sine Function The Lemniscatic Function Basic Identities

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15 The Sine Function The Lemniscatic Function The Addition Law

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17 Multiplication by Integers

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21 Constructions

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25 Abel’s Theorem

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


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