Searching for patterns is a way of thinking that is essential for making generalizations, seeing relationships, and understanding the logic and order of mathematics. Functions evolve from the investigation of patterns and unify the various aspects of mathematics.
About Teaching Mathematics Patterns and Functions (p. 112)
If the cosmos were suddenly frozen, and all movement ceased, a survey of its structure would not reveal a random distribution of parts. Simple geometrical patterns, for example, would be found in profusion—from the spirals of galaxies to the hexagonal shapes of snow crystals. Set the clockwork going, and its parts move rhythmically to laws that often can be expressed by equations of surprising simplicity. And there is no logical or a priori reason why these things should be so.
Order and Surprise Chapter 4 (p. 57)
Jeffers, Robinson ...the old man looked up
At a black eyelet in the white of the Milky Way, and he thought with wonder: "There—or thereabout— Cloaked in thick darkness in his power's dust-cloud, There is the hub and heavy nucleus, the ringmaster Of all this million-shining whirlwind of dancers, the stars of this end of heaven. It is strange, truly, That great and small, the atoms of a grain of sand and the suns of planets, and all the galactic universes Are organized on one pattern, the eternal roundabout, the heavy nucleus and whirling electrons, the leashed And panting runners going nowhere; frustrated flight, unrelieved strain, endless return— all— all—
The eternal fire-wheel."
The Double Axe and Other Poems Part II of The Double Axe The Inhumanist Stanza 22 (p. 67)
In their search for patterns and logical connections, mathematicians face a vast, mysterious ocean of possibilities. Over the centuries, they have discovered an extensive archipelago of truth and beauty. Much of that accumulated knowledge is passed on to succeeding generations. Even more wonders await future explorers of deep, mathematical waters.
Islands of Truth: A Mathematical Mystery Cruise
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