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