Lesson plan
Rectangular function
The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as \operatorname{rect}\left(\frac{t}{T}\right) = \Pi\left(\frac{t}{T}\right) = \left\{\begin{array}{rl} 0, & \text{if } |t| > \frac{T}{2} \\ \frac{1}{2}, & \text{if } |t| = \frac{T}{2} \\ 1, & \text{if } |t| Alternative definitions of the function define \operatorname{rect}\left(t=\pm\frac{T}{2}\right) to be 0, 1, or undefined. The area under the curve does not change for the different definitions of the functions at t=\pm\frac{T}{2} . The rectangular function can be used as the basis for a rectangular wave.
Article summary
The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as \operatorname{rect}\left(\frac{t}{T}\right) = \Pi\left(\frac{t}{T}\right) = \left\{\begin{array}{rl} 0, & \text{if } |t| > \frac{T}{2} \\ \frac{1}{2}, & \text{if } |t| = \frac{T}{2} \\ 1, & \text{if } |t| Alternative definitions of the function define \operatorname{rect}\left(t=\pm\frac{T}{2}\right) to be 0, 1, or undefined. The area under the curve does not change for the different definitions of the functions at t=\pm\frac{T}{2} . The rectangular function can be used as the basis for a rectangular wave.
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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
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.