1. Presented by: Whitney Chadwick, Zachary Dickinson, & Guadalupe Esquivel

2. History Definitions Circles/Shapes The Basics Euclid’s Axioms Distance Applications Conclusion

3. Hermann Minkowski (1864-1909) Karl Menger - 1952 Taxicab Geometry: An Adventure in Non- Euclidean Geometry - 1975

4. Since the distance between two points is now measured by horizontal and vertical lines, it has some implications of other basic elements of geometry. In Euclidean, there was one shortest distance between two points. In taxicab geometry, there are many…

5. The Euclidean definition of a circle is a set of points with a fixed distance from a point. Taxicab circles hold the same property, but look a little different. Also, pi is no longer equal to 3.14, but 4.

7. The Distance Formula The City-Dweller’s Shortest Distance The Distance Impact

8. Review Failed Axiom

9. In Euclidean: The distance between A and D Measured by taking a perpendicular line to the BC through point D

10. In Taxicab Geometry, it’s measured with vertical lines

11. In Euclidean Geometry, the midset is the perpendicular bisector of the line connecting the two points

12. Case 1 Case 2 0<|m|<1

13. Case 3 |m|>1 Case 4 |m|=1

14. Finding the shortest distance between two places 2D video games

15. Why is it significant? How does it relate to our class? ?

16. Thank you for your time!

17. http://strikes.blogs.uny.ac.id/2015/10/ http://jwilson.coe.uga.edu/MATH7200/TaxiCa b/TaxiCab.html http://www.math.iastate.edu/thesisarchive/M SM/JanssenMSMSS07.pdf http://taxicabgeometry.net/