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Subtraction and Integral Introduction

Subtraction and Integral Introduction
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2015-09-16 09:42
CalculusIntegralGeometric Construction
In collections Drawings vs. Constructions
This example demonstrates the basic concepts of subtraction and integral through geometric figures. It first shows the application of subtraction in geometry by constructing a pyramid, and then uses integration to calculate the volume of the pyramid. The commands used in the construction include Polygon, OrthogonalLine, Intersect, Angle, Segment, and Point. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(B, b) → d
  3. Intersect(d, b) → D
  4. Angle(C, D, B) → α
  5. Segment(D, B) → e
  6. Polygon(E, F, G) → poly2, g, e_1, f
  7. Point(g) → H
  8. Segment(H, G) → h
  9. Angle(g, h) → β

AI Drawing Prompt Reference

Draw a triangle, drop a perpendicular from one vertex to the opposite side, mark the foot, connect the foot to that vertex to form a segment, and indicate the angle at the foot; then draw another triangle, pick a point on one of its sides, join that point to the opposite vertex, and show the angle between the side and the new segment. The construction illustrates subtraction and integral concepts geometrically.
The prompt above was compiled from the original drawing commands and is for reference only.