View source for torxesu

==== valsi ====
torxesu
==== type ====
fu'ivla
==== creator ====
[[personal/krtisfranks|krtisfranks]]
==== time entered ====
Thu Sep 22 17:30:10 2016
 
== English ==
=== Definition #68917 - Preferred ===
 
==== definition ====
x<sub>1</sub> is a torus of genus x<sub>2</sub> (li; nonnegative integer), having x<sub>3</sub> (li; nonnegative integer) distinct cusps, and with other properties/characteristics x<sub>4</sub>, by standard/in sense x<sub>5</sub>; x<sub>1</sub> is an x<sub>2</sub>-fold torus.
==== notes ====

The contextless default for <span class="MATH"><i>x</i><sub>3</sub></span> is probably 0. A coffee mug is a 1-fold torus by the standard of topology but not by the standard of geometry. <span class="MATH"><i>x</i><sub>2</sub></span> can be only a nonnegative integer or some sort of infinity. See also: [[cukydjine|cukydjine]], where the material properties and realization of the (physical) object matter.  MATH
 $x_2 = 0, x_3 = 1$
 
<span class="MATH"><i>x</i><sub>2</sub> = 0, <i>x</i><sub>3</sub> = 1</span> means that <span class="MATH"><i>x</i><sub>1</sub></span> is a horn(ed) torus (the cross-section with the two circles has them intersecting at exactly 1 point);  MATH
 $x_0 = 1, x_3 = 2$
 
<span class="MATH"><i>x</i><sub>0</sub> = 1, <i>x</i><sub>3</sub> = 2</span> means that <span class="MATH"><i>x</i><sub>1</sub></span> is a spindle torus (the cross-section with the two circles has them intersecting at exactly 2 points);  MATH
 $x_2 = 0, x_3 =$
 
<span class="MATH"><i>x</i><sub>2</sub> = 0, <i>x</i><sub>3</sub> =</span> [[ro|ro]] means that <span class="MATH"><i>x</i><sub>1</sub></span> 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
 $x_2 = 1, x_3 = 0$
 
<span class="MATH"><i>x</i><sub>2</sub> = 1, <i>x</i><sub>3</sub> = 0</span> means that <span class="MATH"><i>x</i><sub>1</sub></span> 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 ====

<ul><li>[[natlang/en/torus|torus ; mathematically focused]]</li></ul>

==== created by ====
[[personal/krtisfranks|krtisfranks]]
==== vote information ====
1
     
==== time ====
Fri Oct 28 08:36:55 2016



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=== Etymology ===