Difference between revisions of "The Road to Reality Study Notes"
Jump to navigation
Jump to search
The Road to Reality Study Notes (view source)
Revision as of 15:21, 7 June 2020
, 15:21, 7 June 2020→2.6 Historical aspects of hyperbolic geometry
| Line 87: | Line 87: | ||
Penrose makes the point that there are many instances in mathematics where the name attached to a concept is not that of the original discoverer. Some examples given: | Penrose makes the point that there are many instances in mathematics where the name attached to a concept is not that of the original discoverer. Some examples given: | ||
* It is typical to attribute the discovery and first full acceptance of this geometry differing from Euclid’s via the absence of the fifth postulate to Carl Friedrich Gauss, but because Gauss did not publish his work, Janos Bolyai and Nicolai Ivanoivich Lobachevsky are also named as having independently rediscovered this geometry a few decades later. Hyperbolic geometry is frequently referred to as Lobachevskian geometry. | * It is typical to attribute the discovery and first full acceptance of this geometry differing from Euclid’s via the absence of the fifth postulate to Carl Friedrich Gauss, but because Gauss did not publish his work, Janos Bolyai and Nicolai Ivanoivich Lobachevsky are also named as having independently rediscovered this geometry a few decades later. Hyperbolic geometry is frequently referred to as [https://en.wikipedia.org/wiki/Hyperbolic_geometry Lobachevskian geometry]. | ||
* Eugenio Beltrami was mentioned in section 2.5 for the discovery of the relations between the projective and conformal, via the hemispherical realizations. The conformal representation is commonly referred to as the Poincare model and the projective representation as the ‘Klein’ representation after their rediscoveries later in the 19th century. Beltrami is however best known for his [https://en.wikipedia.org/wiki/Pseudosphere#:~:text=In%20geometry%2C%20a%20pseudosphere%20is,immersed%20into%20three%2Ddimensional%20space. pseudo-sphere] representation involving Newton’s [https://en.wikipedia.org/wiki/Tractrix tractrix] curve. | * Eugenio Beltrami was mentioned in section 2.5 for the discovery of the relations between the projective and conformal, via the hemispherical realizations. The conformal representation is commonly referred to as the Poincare model and the projective representation as the ‘Klein’ representation after their rediscoveries later in the 19th century. Beltrami is however best known for his [https://en.wikipedia.org/wiki/Pseudosphere#:~:text=In%20geometry%2C%20a%20pseudosphere%20is,immersed%20into%20three%2Ddimensional%20space. pseudo-sphere] representation involving Newton’s [https://en.wikipedia.org/wiki/Tractrix tractrix] curve. | ||