What is a taxicab circle?

Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. The image to the right shows why this is true, by showing in red the set of all points with a fixed distance from a center, shown in blue.

What is a good value for π in taxicab geometry?

If we adopt the Euclidean definition of pi as the ratio of the circumference of any circle to its diameter, then we have 8r/2r, and the taxicab pi is exactly 4 (Gardner, 1980, p. 23). Taxicab geometry violates another Euclidean theorem which states that two circles can intersect at no more than two points.

How is taxicab geometry different from Euclidean geometry?

The normal kind of geometry we use at school is called Euclidean Geometry. In Euclidean Geometry you measure the distance between two points as being the direct distance as the crow flies, whereas in Taxicab Geometry you are confined to moving along the lines of a grid.

How do you do taxicab geometry?

In Taxicab Geometry, the distance between two points is found by adding the vertical and horizontal distance together. Also, taxicab circles won’t be nice and round. Because of their non-Euclidean geometry, they will have four corners and straight edges instead.

What is a triangle in taxicab geometry?

Definition 5.1 A taxicab triangle incircle, or inscribed circle, is a taxicab circle entirely contained in a triangle with three of its corners touching the sides of the triangle. Theorem 5.2 (Triangle Incircle Theorem) A triangle has a unique taxicab incircle if and only if it is an inscribed triangle.

Why is it called the taxicab metric?

Taxicab geometry gets its name from the fact that taxis can only drive along streets, rather than moving as the crow flies. Euclidian Distance between A and B as the crow flies: 8.49units (Green). Taxicab Distance between A and B: 12 units (Red,Blue and Yellow).

Which distance measures is also called taxicab geometry?

Diameter is the longest possible distance between two points on the circle and equals twice the radius. Circumference is the length of the circle. The same definitions of the circle, radius, diameter and circumference make sense in the taxicab geometry (using the taxicab distance, of course).

How do I find my taxicab angle?

The shortest distance from the origin to the point (1,1) is now 2 rather than √ 2. So, taxicab geometry is the study of the geometry consisting of Euclidean points, lines, and angles in R2 with the taxicab metric d((x1,y1),(x2,y2)) = |x2 − x1| + |y2 − y1|.

How is a circle determined in taxicab geometry?

Circles in discrete and continuous taxicab geometry. A circle is a set of points with a fixed distance, called the radius, from a point called the center. In taxicab geometry, distance is determined by a different metric than in Euclidean geometry, and the shape of circles changes as well.

How are the sides of a taxicab supposed to be?

Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes. The image to the right shows why this is true, by showing in red the set of all points with a fixed distance from a center, shown in blue.

How do you calculate the taxi cab distance?

Taxi cab distance is the sum along a horizontal plus a vertical. If the point Q is on the horizontal with P then h would be the taxicab distance from P to Q. If the point Q is on the vertical with P then v is the taxicab distance from P to Q. The TC distance from P to the line would be the minimum for all points Q on the line.

Which is the shortest path in taxicab geometry?

Taxicab geometry versus Euclidean distance: In taxicab geometry, the red, yellow, and blue paths all have the same shortest path length of 12. In Euclidean geometry, the green line has length 6 2 ≈ 8.49 {\\displaystyle 6{\\sqrt {2}}\\approx 8.49} , and is the unique shortest path.