Search results
Results from the WOW.Com Content Network
The non-orientable genus, demigenus, or Euler genus of a connected, non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − k , where k is the non-orientable genus.
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [2]
The carat was once specified as four grains in the English-speaking world. Some local units in the English dominion were (re-)defined in simple terms of English units, such as the Indian tola of 180 grains. Tod This was an English weight for wool. [32] It has the alternative spelling forms of tode, todd, todde, toad, and tood. [33]
The genus (sometimes called the demigenus or Euler genus) of a connected non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ , via the relationship χ = 2 − g , where g is the non-orientable ...
It has Euler characteristic 1, hence a demigenus (non-orientable genus, Euler genus) of 1. The topological real projective plane can be constructed by taking the (single) edge of a Möbius strip and gluing it to itself in the correct direction, or by gluing the edge to a disk. Alternately, the real projective plane can be constructed by ...
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.
The greater septimal tritone (also Euler's tritone), is an interval with ratio 10:7 [2] (617.49 cents). They are also known as the sub-fifth and super-fourth, or subminor fifth and supermajor fourth, respectively. [3] [4] The 7:5 interval (diminished fifth) is equal to a 6:5 minor third plus a 7:6 subminor third.
When n = 7, the set of all such locations is called 7-dimensional space. Often such a space is studied as a vector space , without any notion of distance. Seven-dimensional Euclidean space is seven-dimensional space equipped with a Euclidean metric , which is defined by the dot product .