torxesu

valsi

torxesu

type

fu'ivla

creator

krtisfranks

time entered

Thu Sep 22 17:30:10 2016  

English

Definition #68917 - Preferred

 

definition

x₁ is a torus of genus x₂ (li; nonnegative integer), having x₃ (li; nonnegative integer) distinct cusps, and with other properties/characteristics x₄, by standard/in sense x₅; x₁ is an x₂-fold torus.

notes

The contextless default for x₃ is probably 0. A coffee mug is a 1-fold torus by the standard of topology but not by the standard of geometry. x₂ can be only a nonnegative integer or some sort of infinity. See also: cukydjine, where the material properties and realization of the (physical) object matter. MATH

$x_2 = 0, x_3 = 1$

x₂ = 0, x₃ = 1 means that x₁ is a horn(ed) torus (the cross-section with the two circles has them intersecting at exactly 1 point); MATH

$x_0 = 1, x_3 = 2$

x₀ = 1, x₃ = 2 means that x₁ is a spindle torus (the cross-section with the two circles has them intersecting at exactly 2 points); MATH

$x_2 = 0, x_3 =$

x₂ = 0, x₃ = ro means that x₁ is a sphere (the cross-section with the two circles has them intersecting at all of their points (which also is uncountably infinitely many) so that they are mutually indistinguishable); MATH

$x_2 = 1, x_3 = 0$

x₂ = 1, x₃ = 0 means that x₁ is a standard/basic torus (the cross-section with the two circles has them intersecting at exactly 0 points; the result is a classic 'donut' shape).

gloss words

• torus ; mathematically focused

created by

krtisfranks

vote information

1

time

Fri Oct 28 08:36:55 2016

Examples

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