Square (EntityTopic, 20)
From Hi.gher. Space
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*The [[radial slice]]s ''θ'' of a square are: | *The [[radial slice]]s ''θ'' of a square are: | ||
<blockquote>[:x,:y] ⇒ [[line segment]] of length ''l''sin(45° + (''θ'' % 90°)√2</blockquote> | <blockquote>[:x,:y] ⇒ [[line segment]] of length ''l''sin(45° + (''θ'' % 90°)√2</blockquote> | ||
| + | |||
| + | == Segmentation == | ||
| + | The square of side 2 may be [[segment]]ed into 4× [[triangle]] with sides 2, 2×2<sup>2<sup>-1</sup></sup> and angles 2×45°, 90°. | ||
{{Dishapes}} | {{Dishapes}} | ||
{{Rotope Nav|1|2|3|I<br>Line segment|II<br>Square|I'<br>Triangle|gons}} | {{Rotope Nav|1|2|3|I<br>Line segment|II<br>Square|I'<br>Triangle|gons}} | ||
{{Bracketope Nav|1|2|3|x<br>Line segment|[xy]<br>Square|<xy><br>Diamond|gons}} | {{Bracketope Nav|1|2|3|x<br>Line segment|[xy]<br>Square|<xy><br>Diamond|gons}} | ||
Revision as of 16:49, 16 September 2007
A square is a two-dimensional hypercube.
Squares are the most common base for two-dimensional manifolds and polyominoes.
Geometry
Equations
- Variables:
l ⇒ length of edges of the square
- The radial slices θ of a square are:
[:x,:y] ⇒ line segment of length lsin(45° + (θ % 90°)√2
Segmentation
The square of side 2 may be segmented into 4× triangle with sides 2, 2×22-1 and angles 2×45°, 90°.
| Notable Dishapes | |
| Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
| Curved: | circle |
| 1. x Line segment | 2. [xy] Square | 3. Diamond |
| List of bracketopes | ||
