CENSUS OF FOUR SQUARE FEET

Quarternions and the Four Square Theorem

The Four Square Theorem was proved by Lagrange in 1770: every positive integer is the sum of at most four squares of positive integers, i.e. n = A2 + B2 + C2 + D2, A, B, C, D ∈ Z An interesting proof is presented here based on Hurwitz integers, a subset of quarternions which act like integers in four dimensions and have the prime divisor property. It is analogous to Fermat’s Two Square Theorem,...

Fair and square: the four sides of distributive justice

Recent theoretical progress on inequity has left unresolved the crucial question of what constitutes equity. This paper proposes a positive theory of distributive justice, in a framework of inequity aversion, that depends on three general justice principles and context. The current study challenges the view of many previous inquiries that justice is context-specific and instead advances a theor...

Planar graphs with square or cube root are four-colorable

Four square step test performance in people with Parkinson disease.

BACKGROUND AND PURPOSE The Four Square Step Test (4SST), a quick and simple test of multidirectional stepping, may be useful in predicting falls in people with Parkinson disease (PD). We studied the reliability of the 4SST and its ability to discriminate between freezers and nonfreezers, between fallers and nonfallers, and factors predictive of 4SST performance in people with PD. METHODS Fift...

Severe Gram-Negative Intertrigo of the Feet

Introduction: Intertrigo is a common disease of the skin usually caused by fungi and/or bacteria, often involving major or minor skin folds. Here, we report a case of severe, ulcerative intertrigo of all interdigital folds of both feet caused by Pseudomonas aeruginosa in a patient with type II diabetes who acquired the infection during a trip to Senegal. Case Pres...