
Resources

Definition
Lagrange's foursquare theorem: Every nonnegative integer can be expressed as the sum of four squares.
For example:
9 = 1^{2} + 2^{2} + 2^{2} + 0^{2}
36 = 5^{2} + 3^{2} + 1^{2} + 1^{2}
Background Information
 Lagrange's foursquare theorem  Wikipedia [View Resource]
 Lagrange's FourSquare Theorem  MathWorld [View Resource]
 AdrienMarie Legendre Life and Work [View Resource]
K12 Lesson Plans, Proofs and Science Fair Projects
 Lagrange's foursquare theorem proof [View Resource]
 An applet decomposing numbers as sums of four squares [View Resource]

A New Method to Prove Euler's Equation by Using the Lagrange Mean Value Theorem[View Resource]
 Lagrange Four Square Theorem (Bachet Conjecture) Calculation ind Instructions [View Resource]
 Lagrange's Four Square Theorem Proof [View Resource]
Undergraduate Lesson Plans, Proofs, Studies and Articles
 Representations of binary forms by quinary quadratic forms [View Resource]
 Lagrange's foursquare theorem proof using convex geometry [View Resource]
 A Proof of Lagrange's Four Square Theorem Using Quaternion Algebras [View Resource]
 Cosets and Cardinality Lesson [View Resource]
 Patterns in Prime Numbers: The Quadratic Reciprocity Law [View Resource]
Theses and Dissertations
 Convex functions and optimization techiniques [View Resource]
 Automatic Formulation of Lagrangian DAEs [View Resource]

