“Integral geometry, started by the English geometer M. W. Crofton, has received recently important developments through the works of W. Blaschke, L. A. Santaló, and others. Generally speaking, its principal aim is to study the relations between the measures which can be attached to a given variety.”

[Differential geometry and integral geometry, Proc. Int. Congr. Math. Edinburgh, 1958, 411–449, http://www.mathunion.org/ICM/ICM1958/Main/icm1958.0441.0453.ocr.pdf]

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Integral geometry, started by the English geometer M. W. Crofton, has received recently important developments through …" by Shiing-Shen Chern?
Shiing-Shen Chern photo
Shiing-Shen Chern 6
mathematician (1911–2004), born in China and later acquirin… 1911–2004

Related quotes

Hermann Weyl photo

“Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself.”

Hermann Weyl (1885–1955) German mathematician

On the foundations of general infinitesimal geometry. Bull. Amer. Math. Soc. 35 (1929) 716–725 [10.1090/S0002-9904-1929-04812-2] (quote on p. 716)

Henry John Stephen Smith photo
Carl Friedrich Gauss photo
René Descartes photo

“(a) There is a general tendency towards integration in the various sciences, natural and social. (b) Such integration seems to be centered in a general theory of systems. (c) Such theory may be an important means of aiming at exact theory in the nonphysical fields of science. (d) Developing unifying principles running "vertically" through the universe of the individual sciences, this theory brings us nearer to the goal of the unity of sciences. (e) This can lead to a much needed integration in scientific education.”

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

Variant: Mayor aims of general theory:
(1) There is a general tendency toward integration in the various sciences, natural and social.
(2) Such integration seems to be centered in a general theory of systems.
(3) Such theory may be an important means for aiming at exact theory in the nonphysical fields of science.
(4) Developing unifying principles running "vertically" through the universe of the individual sciences, this theory brings us nearer the goal of the unity of science.
(5) This can lead to a much-needed integration in scientific education.
Source: 1950s, "General systems theory," 1956, p. 38, cited in: Alexander Laszlo and Stanley Krippner (1992) " Systems Theories: Their Origins, Foundations, and Development http://archive.syntonyquest.org/elcTree/resourcesPDFs/SystemsTheory.pdf" In: J.S. Jordan (Ed.), Systems Theories and A Priori Aspects of Perception. Amsterdam: Elsevier Science, 1998. Ch. 3, pp. 47-74.

Francis Heylighen photo

“W. Ross Ashby is one of the founding fathers of both cybernetics and systems theory. He developed such fundamental ideas as the homeostat, the law of requisite variety, the principle of self-organization, and the principle of regulatory models.”

Francis Heylighen (1960) Belgian cyberneticist

" Ashby's book "Introduction to Cybernetics http://pespmc1.vub.ac.be/ASHBBOOK.html" at Principia Cybernetica Web, 1999-2003
Principia Cybernetica Web, 1999-2003

Russell L. Ackoff photo
Hans Reichenbach photo
Richard von Mises photo

Related topics