MathPlotAI Logo MathPlotAI

Vertical Partitions - Square vs. Circle

Vertical Partitions - Square vs. Circle
Loading the math board and drawing, please wait…
2018-02-27 03:06
CirclePolygonFunctionCoordinate GeometryCalculus
This example demonstrates the comparison of vertical partitions between a square and a circle. It involves core mathematical concepts such as circle, fractions, square, median value, indefinite integral, subtraction, cylinder, and rotation. The construction uses GeoGebra commands like Circle, Sequence, Zip, and Polygon. It is suitable for high school students and educators to understand geometric and calculus concepts.

GeoGebra Commands & Parameters

  1. Circle((0.5, 0), 0.5) → c
  2. Sequence(i / Denominator, i, 1, Denominator - 1) → squareXs
  3. Sequence(h(x) - (i / Denominator * Area[c]) - h(0), i, 1, Denominator - 1) → L_4
  4. Zip(x(Root[AA, 0]), AA, L_4) → circleXs
  5. Zip((AA * (1 - circlePartitions)) + (BB * circlePartitions), AA, squareXs, BB, circleXs) → movingXs
  6. Polygon((0, -1 / 2), (1, -1 / 2), 4) → poly1
  7. Sequence(Segment[(i / Denominator, -1 / 2), (i / Denominator, 1 / 2)], i, 1, Denominator - 1) → L_2
  8. Sequence(Segment[(i / Denominator, f(i / Denominator)), (i / Denominator, (-f(i / Denominator)))], i, 0, Denominator) → L_3
  9. Zip(Segment[(AA, f(AA)), (AA, (-f(AA)))], AA, circleXs) → L_5
  10. Zip(Segment[(AA, (f(AA) * circleLength) + (0.5 * squareLength)), (AA, ((-f(AA)) * circleLength) - (0.5 * squareLength))], AA, movingXs) → L_6

AI Drawing Prompt Reference

Draw a square and a circle to compare their vertical partitions. The square is divided into multiple rectangles with decreasing widths, while the circle is divided into sectors with decreasing arc lengths. Use distinct colors or line styles to differentiate the partitions within the square and circle, highlighting the geometric and calculus concepts involved.
The prompt above was compiled from the original drawing commands and is for reference only.