Lesson plan
Hyperrectangle
In geometry, a hyperrectangle (also called a box, hyperbox, k -cell or orthotope ), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. This means that a k -dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k -cell is compact. If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope.
Article summary
In geometry, a hyperrectangle (also called a box, hyperbox, k -cell or orthotope ), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. This means that a k -dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k -cell is compact. If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.