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Arctan Identity for Pi/2

Arctan Identity for Pi/2
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2019-10-28 22:45
FunctionTrigonometrySequenceCalculusGeometric Construction
This example demonstrates the geometric representation of the infinite sum of arctangents equating to pi/2 using GeoGebra. It involves core math concepts like arctangent functions, infinite sequences, trigonometry, and integral calculus. The construction utilizes the Sequence command to generate the arctangent values in the infinite series. Suitable for high school and above students to explore the relationship between infinite series and trigonometric functions geometrically.

GeoGebra Commands & Parameters

  1. Sequence(atand(1 / sqrt(i)), i, 1, n) → l1
  2. Sequence(Sum[l1(k), k, 1, i], i, 1, n) → l2
  3. Sequence(If[i < 1, (1, 0), Vector[(sqrt(i) * (cos(l2(i)), sin(l2(i))))]], i, 0, n) → l3
  4. Sequence(Polygon[(0, 0), l3(i), l3(i + 1)], i, 1, n) → l4