GNOMONS GENERATE STRUCTURES. MATH IS MOSTLY GNOMONS AND THEIR CLOSURE INTO PATTERNS. GENERATIVE MATH (UNLIKE AXIOMATIC MATH) EXPLICATES THIS.

TABLE OF GNOMONS (GENERATORS OF STRUCTURE)
GNOMONSTRUCTUREEXAMPLECOMMENT
POINTS/DOTS AS GENERATORSFIGURATE GEOMETRY OF NUMBERSODD NATURAL NUMBERS
GENERATE SQUARES:
1+3 = 4 = 22;
1+3+5 = 9 = 32;
1+3+5+7=16=42		DUE TO PYTHAGORAS
EIGENVALUES, EIGENVECTORSINDEPENDENT MODES OF OSCILLATORENERGY LEVELS OF ELECTRONSFROM L. EULER
TO ERWIN
SCHRÖDINGER
NUMBER/NAME SETS(BINARY) RELATIONS, FUNCTIONS, OPERATIONSORD. PR. WITH COMPONENTS FROM SAME SET IS OPERATIONCOMPREHENDS MUCH OF MATHEMATICS
GREEN'S FUNCTIONPOINT SOURCE PRODUCING NEARBY POTENTIALELECTRIC CHARGE, OR PROPAGATORFROM T. GREEN TO R. FEYNMAN
INNER PRODUCT VECTOR SPACEIMPLICATES INDEPENDENT VECTORS<1,0>.<0,1> = 0EXTENDS TO ORTHOGONAL CONTINUOUS FUNCTIONS
NTL. NOS.; ORD. PRS. NTL. NOS.; ORD PRS OF ORD PRS OF NTL NOS; ETC.NATURALS; INTEGERS; RATIONALS; REALS; ETC.FOR NATURALS,
<0,4> = _ 4;
FOR INTEGERS,
<a,b> = a/b;		CALLED "KRONECKER PROGRAM", BUT INITIATED BY W. R. HAMILTON
SINE/COSINE FUNCTIONSSERIES (INTEGRAL) GENERATION OF PERIODIC (NONPERIODIC) FUNCTIONSFAST FOURIER TRANSFORMBY WEIERSTRASS' THEOREM, CAN GENERATE ANY X-FUNCTION
TYPONS, ORDONS, LINEAONS, RATIONSGENERATE TYPOLOGICAL,ORDINAL, LINEAR, RATIO MEASURESDUE TO PSYCHO-
PHYSICIST S. S. STEVENS
ODD NATURAL NUMBERSSQUARES1+3+5=4=22DUE TO PYTHGAGORAS