Absolute Geometry

Geometry which depends only on the first four of Euclid's Postulates and not on the Parallel Postulate. Euclid himself used only the first four postulates for the first 28 propositions of the Elements">Elements, butwas forced to invoke the Parallel Postulate on the 29th.

References

Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, pp. 90-91, 1989.

• Helmholtz Differential Equation--Cartesian Coordinates
• Helmholtz Differential Equation--Circular Cylindrical Coordinates
• Helmholtz Differential Equation--Confocal Ellipsoidal Coordinates
• Helmholtz Differential Equation--Confocal Paraboloidal Coordinates
• Helmholtz Differential Equation--Conical Coordinates
• Helmholtz Differential Equation--Elliptic Cylindrical Coordinates
• Helmholtz Differential Equation--Oblate Spheroidal Coordinates
• Helmholtz Differential Equation--Parabolic Coordinates
• Helmholtz Differential Equation--Parabolic Cylindrical Coordinates
• Helmholtz Differential Equation Polar Coordinates
• Helmholtz Differential Equation--Prolate Spheroidal Coordinates
• Helmholtz Differential Equation--Spherical Coordinates
• Helmholtz Differential Equation--Spherical Surface
• Helmholtz Differential Equation--Toroidal Coordinates
• Helmholtz's Theorem
• Helson-Szegö Measure
• Hemicylindrical Function
• Hemisphere
• Hemispherical Function
• Hempel's Paradox
• Hendecagon
• Henneberg's Minimal Surface
• Hensel's Lemma
• Henstock-Kurzweil Integral
• Heptacontagon