MathPlotAI Logo MathPlotAI

Parallelogram Circumcircle and Power Functions Interactive Exercise

Parallelogram Circumcircle and Power Functions Interactive Exercise
Loading the math board and drawing, please wait…
2017-06-14 18:04
CirclePolygonFunctionCalculusGeometric Construction
In collections LINEAR FUNCTIONS
① This interactive GeoGebra example demonstrates a parallelogram with its circumcircle, linked to power function graphs, forming a multi-concept exercise. ② Core mathematical concepts include properties of parallelograms, conditions for a cyclic quadrilateral (circumcircle), power functions and their graphs, and the connection between algebraic expressions and geometric figures. ③ Construction details: uses Random and RandomElement to generate random parameters, Textfield and InputBox for user input, TableText for data display; objects include a, b, ab, n, button1, g, c, h, A1, InputBox1, f, d, etc., involving points, lines, circles, function graphs, and button controls to trigger random changes. ④ Suitable for high school or pre-university students, for introductory calculus (power functions) combined with plane geometry practice, and useful as a classroom demonstration or self-paced interactive exercise.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → a
  2. Random(-10, 10) → b
  3. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c
  4. Textfield(h) → InputBox1
  5. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → a_1
  6. Random(-10, 10) → b_1
  7. RandomElement({-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}) → c_1
  8. Random(-10, 10) → d_1
  9. Textfield(m) → InputBox2
  10. TableText({{A1_1, B1_1, C_1, D_1}, {-3, g(-3), h(-3), f(-3)}, {-2, g(-2), h(-2), f(-2)}, {-1, g(-1), h(-1), f(-1)}, {0, g(0), h(0), f(0)}, {1, g(1), h(1), f(1)}, {2, g(2), h(2), f(2)}, {3, g(3), h(3), f(3)}, {p, e, l, k}}, "|_r") → text3_1

AI Drawing Prompt Reference

Draw a parallelogram with its circumcircle passing through all four vertices. In the same coordinate system, plot three power function curves in distinct colors. Include two input fields for adjusting parameters and a table showing function values at several integer points. Add a button that randomly changes parameters to update the shapes and curves dynamically. Arrange the geometry on the left and the function graphs with the data table on the right for comparison.
The prompt above was compiled from the original drawing commands and is for reference only.