Infinite Geometry

Projective Geometry and Infinite Relations

Three Relations of Infinity
Theorems of projective geometry at infinite scales

Infinite geometry theorems apply the principles of projective geometry to understand how geometric relationships behave at infinite scales. These proofs reveal fundamental properties of angles, curves, and transformations when extended to infinity.

90 Degree Angles
Orthogonal relationships in projective infinite geometry

This theorem explores how right angles and orthogonal relationships behave in projective geometry when extended to infinity. It reveals surprising properties about perpendicularity at infinite scales and how angular relationships are preserved or transformed.

Key Concepts

  • Orthogonality preservation in projective transformations
  • Right angle behavior at points at infinity
  • Angular invariants in infinite projective space
  • Relationship between Euclidean and projective angles
View full proof on GitHub
Differentiation and Acceleration
Calculus concepts extended to infinite geometric systems

This theorem extends differential calculus into projective infinite geometry, exploring how rates of change and acceleration behave at infinite scales. It bridges analysis and geometry, revealing deep connections between calculus and projective transformations.

Key Concepts

  • Differential geometry at points at infinity
  • Acceleration and curvature in infinite projective space
  • Tangent spaces and derivatives at infinity
  • Geometric interpretation of higher-order derivatives
View full proof on GitHub
Projective Framework

Infinite geometry represents the third fundamental approach to understanding infinity in the Laegna framework. By applying projective geometry principles, these theorems reveal how geometric relationships extend naturally to infinite scales.

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