Geometry: An Interactive Journey to Mastery

Lesson 36: Bending the Axioms—New Geometries

Solution

D௘ͽ 'LVWDQFH  

E௘ͽ 'LVWDQFH  

F௘ͽ 'LVWDQFH  515 606.76 611.96.

Example 2

D௘ͽ 3ORWWKHSRLQWVA ͼ௘௘ͽDQGB ͼ௘௘ͽ

E௘ͽ )LQGDSRLQWP whose taxicab distance from A is the same as its taxicab distance from B,QIDFW¿QG

such points. Actually, graph the set of all points that are equidistant from A and B in taxicab geometry.

ͼ௘7KLVLVWKHWD[LFDEYHUVLRQRIWKHSHUSHQGLFXODUELVHFWRURIAB௘ͽ

Solution

This graph is surprising!

Study Tip

x This lesson is purely optional. There are no recommended study tips for this lesson other than to enjoy

the lesson and let the thinking about it strengthen your understanding of geometry as a whole.

Pitfall

x Don’t forget to have fun in your thinking of mathematics. This is a fun topic.

x

y

A

B

Figure 36.1