Harnack's Theorems

Harnack's first theorem states that a real irreducible curve of order cannot have more than

Harnack's second theorem states that there exists a curve of every order with the maximum number of circuits compatible withthat order and with a certain number of double points, provided that number is not permissible for a curve of lower order(Coolidge 1959, p. 61).

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, 1959.

• Source
• Sous-Double
• Souslin Set
• Souslin's Hypothesis
• Sous-Triple
• Space
• Space Conic
• Space Curve
• Space Diagonal
• Space Distance
• Space Division
• Space-Filling Curve
• Space-Filling Function
• Space-Filling Polyhedron
• Space Groups
• Space of Closed Paths
• Span (Geometry)
• Span (Link)
• Span (Polynomial)
• Span (Set)
• Span (Vectors)
• Sparse Matrix
• Spearman Rank Correlation Coefficient
• Special Curve
• Special Function