Lesson plan
Arc length
as a function of its parameter θ Arc length is the length of a curve from beginning to end. Conceptually, if we imagined the curve as a string, the arc length is how long the string would be if we straightened it out. It can be formalized mathematically for smooth curves using vector calculus and differential geometry, or for curves that might not necessarily be smooth as a least upper bound of lengths of polygonal chains. The curves for which this limit exists are called rectifiable curves, and the process of determining their arc length in this way is called curve rectification.
Article summary
as a function of its parameter θ Arc length is the length of a curve from beginning to end. Conceptually, if we imagined the curve as a string, the arc length is how long the string would be if we straightened it out. It can be formalized mathematically for smooth curves using vector calculus and differential geometry, or for curves that might not necessarily be smooth as a least upper bound of lengths of polygonal chains. The curves for which this limit exists are called rectifiable curves, and the process of determining their arc length in this way is called curve rectification.
Key claims
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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.