26 Jan 2003 version Michael Somos
Here is a list of some entry points to the Elliptic Realm:

 1. Rectification of Ellipse leads to Elliptic integral of second kind.
 2. Rectification of Lemniscate leads to Lemniscate integral ala Gauss.
 3. Addition theorem of Elliptic integrals ala Euler.
 4. Simple pendulum dynamics leads to Jacobi elliptic functions ala Greenhill.
 5. Spherical triangle law of cosines leads to cn() addition theorem ala Study.
 6. Spherical spiral with arc length linear function of longitude ala Sieffert.
 7. Discrete version of spherical spiral based on ambiguous spherical triangle.
 8. Poncelet porism of in/circum-scribed polygons in circles ala Kerawala.
 9. Doubly periodic meromorphic complex analytic functions are elliptic.
10. Analytic functions with algebraic addition theorems are elliptic.
11. Theta functions as solution of periodic heat equation with delta function.
12. Theta functions as products of q-expansions with trig factors.
13. Ramanujan theta function sum in two variables (Somos extension to three).
14. Gauss AGM process leads to theta constant functions and theta functions.
15. Congruent number problem: Heronian triangle with fixed area.
16. Elliptic curve addition of points leads to division polynomials.
17. Unification of circular+hyperbolic addition theorem yields Somos sequences.
18. Coupled non-linear differential equation yields sn/cn/dn ala Schett.
19. Somos-4 number wall ala David Cantor yield division polynomials.
20. Pfaffian triple equations leads to divisibility sequences ala Somos.
21. Pfaffian triples leads to functional equations for power series ala Somos.
22. Quadruple sequences model theta/sigma function recurrences ala Moutard.
23. Weierstrasss p-function as double sum obviously doubly periodic.
24. Jacobi elliptic functions based on inversion ala Jacobi Fundamenta Nova.
25. Heisenberg group global oscillator representation, Discrete Fourier xform.
26. Ramanujan's continued fraction and Rogers-Ramanujan identity.
27. Jacobi triple product identity connects infinite product and sum.
28. Lyness 5-cycle + Pentagramma Mirificum generalized recursive sequences.
29. Somos-4 polynomials and generalizations.
30. Jim Propp cubic + octohedron multivariable Laurent recurrences.
31. Biquadratic 2-2 correspondence alternation leads to elliptic sequences.
32. Nonlinear differential equations for sigma/theta functions ala Somos.
33. Non-integer radix expansions and modular functions ala Somos.
34. General theta series as in Somos-6. Forsythe double theta functions.
35. Solitons in nonlinear differential equations  has cnoidal wave solutions.
36. Addition theorem for Jacobi Z and sn lead to elliptic sequences ala Somos.
37. Infinite dimensional spherical curve gives cn() addition theorem ala Somos.
38. Modular function conformal mapping properties, Ford circles, Klein+Fricke.
39. Summation of reciprocal of Lucas numbers leads to theta constant sum.
40. Generating function of partition function, Euler transform, Dedekind eta.