Joshua M. Sabloff – MathCircles.org

Optimal Locations of Firehouses (Taxi-cab Metric)

By:

Topic(s):

Algebra / Arithmetic, Geometry, Problem Solving / General

Supporting Resources:

This session asks participants to expand their notion of “distance,” using a nontraditional taxicab metric instead of the usual Pythagorean notion. Participants are guided to construct the equivalent of “circles” with this new metric and to look at the intersections of multiple such circles. In particular, two firehouses in Gridtown...

Pick’s Theorem

By:

Aimee S. Johnson, Joshua M. Sabloff, Tom Davis

Topic(s):

Geometry

Supporting Resources:

Facilitator Guides, Handouts, Virtual Tools

Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter...

Hercules and the Hydra

By:

Joshua M. Sabloff

Topic(s):

Combinatorics

Supporting Resources:

Facilitator Guides

After a late night reading about classical mythology (or watching “Clash of the Titans” yet again), you drift off to sleep and dream that you are face-to-face with a many-headed monster that is clearly not happy to see you, either. “Ahah,” you think, “I must be Hercules and that ....

I Walk the Line

By:

Aimee S. Johnson, Joshua M. Sabloff

Topic(s):

Combinatorics, Mathematical Modeling, Problem Solving / General

Supporting Resources:

Facilitator Guides, Photos & Videos, References

Your regular commute begins at your house and ends at your office at the corner of 5th street and 6th avenue. You have been making this trip for years, but you are the restless (or adventurous) type, and you try to take a different route each day. At some point,...

Activity Database

Optimal Locations of Firehouses (Taxi-cab Metric)

Pick’s Theorem

Hercules and the Hydra

I Walk the Line