Simulation
Simulation - Discover Pi
Discover the digits of 𝜋 using Newton’s generalized binomial expansion and integration, seeing how the estimate slowly converges, increasing in accuracy as more terms are added.
Unit: Infinite Sequences and Series (AP Calc BC Unit 10)
Topics: Taylor & Maclaurin Series, Interval of Convergence, Error Bounds
In this three-part worksheet, students solve problems based on the ideas of three figures who shaped Newton’s thinking: Isaac Barrow, John Wallis, and René Descartes. Each part connects a historical figure’s work to a core series technique. Students construct and manipulate Maclaurin series to approximate integrals, use the binomial series to derive a series representation for , and build Taylor polynomials with error bounds to approximate cos(1).
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Interactive Work
Interactive embeds and supporting notes for this assignment.
Simulation
Discover the digits of 𝜋 using Newton’s generalized binomial expansion and integration, seeing how the estimate slowly converges, increasing in accuracy as more terms are added.
