Set of Points Equidistant from Two Points in Taxicab Geometry

In taxicab geometry, the usual Euclidean distance between points is replaced by the sum of the absolute differences of their coordinates. In symbols, if the two points are and , the distance between them is . The taxicab distance is also called Manhattan distance or rectilinear distance.
Drag the two red points (discretized only to help in checking) to see the set of points equidistant to them, which forms the "bisector line" of the segment joining the points. If the two points are different, there are three possibilities for this "line":
1. When the line through the points has slope 0 or ∞, coincides with the usual Euclidean bisector line.
2. When the line through the points has slope , takes the shape of two infinite square regions (colored in blue) joined by a line segment.
3. Otherwise, forms a zigzag line.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+