
As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594
Source: Infinite in All Directions (1988), Ch. 2 : Butterflies and Superstrings, p. 17
Context: Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry?... It cannot be answered by a definition.
As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594
Source: Textual politics: Discourse and social dynamics, 1995, p. 2
Source: Infinite in All Directions (1988), Ch. 2 : Butterflies and Superstrings, p. 17
Context: Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry?... It cannot be answered by a definition.
Pattern Integrity 505.201 http://www.rwgrayprojects.com/synergetics/s05/p0400.html#505
1970s, Synergetics: Explorations in the Geometry of Thinking (1975), "Synergy" onwards
September 1874, Popular Science Monthly Vol. 5, Article: The Alleged Antagonism Between Growth and Reproduction , p. 607
The Alleged Antagonism Between Growth and Reproduction (1874)
“Each part in itself constitutes the whole to which it belongs.”
Source: The Cave (2000), p. 68 (Vintage 2003)
“If geometry exists, arithmetic must also needs be implied”
Nicomachus of Gerasa: Introduction to Arithmetic (1926)
Context: If geometry exists, arithmetic must also needs be implied... But on the contrary 3, 4, and the rest might be 5 without the figures existing to which they give names. Hence arithmetic abolishes geometry along with itself, but is not abolished by it, and while it is implied by geometry, it does not itself imply geometry.<!--Book I, Chapter IV