ProofWiki
ProofWiki is an extensive online encyclopedia of mathematical proofs, particularly strong in abstract algebra and discrete mathematics. It aims to provide rigorously verifiable proofs for a wide range of mathematical theorems, making it a valuable resource for students and researchers seeking to understand the logical underpinnings of mathematical concepts.
Overzicht
Toegevoegd op
17 maart 2026
Vak & domein
computer-science-fundamentals · discrete-mathematics
Schooljaar
Klas 1 (brugklas)–Klas 4
Paginatype
Wiki
Inleiding
ProofWiki: Cycloid Arc Length Derivation
- Project Overview: ProofWiki is an online collaborative compendium dedicated to the collection, classification, and creation of mathematical proofs.
- Subject Matter: The provided text details a historical and mathematical derivation of the arc length of a cycloid.
- Mathematical Context:
- The cycloid is defined by parametric equations.
- The goal is to prove that the length of one arc of a cycloid is $8a$.
- Methodology:
- The proof utilizes Descartes' method of approximating the cycloid using a polygon inscribed in a generating circle.
- The derivation involves calculating the lengths of "arms" (chords) formed by the polygon's sides as it rotates.
- Key mathematical tools used include the Inscribed Angle Theorem, Lagrange's Sine Identity, and trigonometric limits.
- Key Result: The total arc length is derived by summing the chord lengths and taking the limit as the number of sides ($n$) approaches infinity.
Community-recensies
Nog geen gepubliceerde recensies. Deel als eerste uw ervaring.