THE MATHEMATICAL BASIS OF THE ARTS RESTFULNESS AND RESTLESSNESS IN A LANDSCAPE As effected by a sine-curve and a complex curve. THE MATHEMATICAL BASIS OF THE ARTS BY JOSEPH SCHILLINGER Part One SCIENCE AND ESTHETICS Part Two THEORY OF REGULARITY AND COORDINATION Part Three TECHNOLOGY OF ART PRODUCTION PHILOSOPHICAL LIBRARY NEW YORK Copyright, 1948, by FRANCES SCHILLINGER All rights reserved International Copyright Secured PRINTED IN THE UNITED STATES OF AMERICA TO MY BELOVED WIFE FRANCES for her unswerving confidence in the permanent value of this work J. S. February 27, 1943