Description
Exploring π in Taxicab Geometry is an interactive tool designed for understanding Taxicab geometry concepts. The applet allow users to resize a “circle” and adjust a line segment to align with a side of a square. As users modify these elements, the applet computes the circumference of the “circle”, taxicab distance of line segment AB, and the value of π specific to `taxicab metric'. Overall, this applet provides a hands-on, visual exploration of Taxicab geometry, enabling users to observe the relationships between “circle” size, circumference, distances, and the unique value of π within this alternate geometry.
Instructions
- Drag the slider, s, to create a “circle” in Taxicab geometry.
- Align segment, AB, to one side of the square either by (1) dragging point A and B or (2) inputting the desired ordered pair for A and B.
- Using the ordered pair fo A and B, see if you can determine the taxicab distance, circumference, and value oof π.
- Check the “Show taxicab distance” box to see point C. Look at the y - value. This is the circumference of the “circle” or perimeter of the square.
- Check the “Show circumference box to see the distance of AB. This is the distance needed to get from point A to point B and vice versa.
- Check the “Show π” to see the value of π. What can you conclude about π in Taxicab geometry?.