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Constructions on the Lemniscate

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

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

2 What is the lemniscate?

3 What is the lemniscate?

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

5 Arc Length

6 Arc Length

7 Arc Length

8 Arc Length

9 The Lemniscatic Function

10 The Lemniscatic Function

11 The Lemniscatic Function
The Sine Function The Lemniscatic Function

12 The Lemniscatic Function
Basic Identities The Sine Function The Lemniscatic Function

13 Basic Identities

14 Basic Identities

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

16 The Addition Law

17 Multiplication by Integers

18 Multiplication by Integers

19 Multiplication by Integers

20 Multiplication by Integers

21 Constructions

22 Constructions

23 Constructions

24 Constructions

25 Abel’s Theorem

26 Abel’s Theorem

27 Abel’s Theorem

28 Abel’s Theorem

29 Abel’s Theorem

30 Abel’s Theorem

31 Abel’s Theorem

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


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