Interactive Euler's Totient Function Demo: Counting Coprime Integers

Interactive Euler's Totient Function Demo: Counting Coprime Integers
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2021-08-20 19:30
This GeoGebra example demonstrates Euler's totient function φ(n), visually showing the count of positive integers less than or equal to n that are coprime to n. Core mathematical concepts include: definition of Euler's totient function in number theory, congruence relations, and determining coprime numbers. Construction details from summary: Unique command for distinct values, If statements for conditional logic, Textfield for user input; objects include Setup (initial setup), n (input parameter), F (function object), phi (totient value), Inp (input control), text (display). Suitable for high school and above, ideal for introductory number theory teaching, function concept expansion, or as reference for programming totient algorithms.

GeoGebra Commands & Parameters

  1. Unique(PrimeFactors[n]) → F
  2. If(n ≤ 0, NaN, If[n ≟ 1, 1, (n * Product[Zip[1 - 1 / p, p, F]])]) → phi
  3. Textfield(n) → Inp

AI Drawing Prompt Reference

Create an interactive demonstration of Euler's totient function φ(n), which shows the count of positive integers less than or equal to n that are coprime to n. First, set up an input field Inp for the user to enter the value of n. Then, calculate φ(n) based on the value of n: if n is less than or equal to 0, display NaN; if n is 1, φ(n) is 1; otherwise, φ(n) is n multiplied by the product of (1-1/p) for all prime factors p of n.
The prompt above was compiled from the original drawing commands and is for reference only.