answersLogoWhite

0

The value of pi in taxicab geometry technically does not exist as any taxicab shape would consist of right angles. A circle does not contain any right angles, therefore circles do not exist in taxicab geometry (so neither does the value pi).

However, if you were to place a square around a circle with diameter 1, where each side is a tangent to the circle and then removed the corners of the square repeatedly without ever removing any or the area of the circle (see Figure 1), the value of 'pi' in that case would be 4 (as pi = diameter/circumference (or in this case perimeter)).

Figure 1

Here the problem arises, as perimeter and circumference are not exactly the same thing. Circumference only pertains to a circle (and circles do not exist in taxicab geometry) whereas perimeter pertains to any geometric shape (whether in taxicab geometry or Euclidean geometry).

User Avatar

Wiki User

13y ago

Still curious? Ask our experts.

Chat with our AI personalities

JudyJudy
Simplicity is my specialty.
Chat with Judy
RossRoss
Every question is just a happy little opportunity.
Chat with Ross
TaigaTaiga
Every great hero faces trials, and you—yes, YOU—are no exception!
Chat with Taiga

Add your answer:

Earn +20 pts
Q: What should the value of pi be in taxicab geometry?
Write your answer...
Submit
Still have questions?
magnify glass
imp