Geometry – MathCircles.org

Stomachion (Archimedes’ Box)

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Facilitator Guides, Featured in MCircular, Handouts, Lesson Plan, References

The Stomachion puzzle, attributed to the Ancient Greek scholar Archimedes and preserved within the Archimedes Palimpsest, is considered to be the oldest known mathematical puzzle. The puzzle contains 14 pieces in 12 distinct shapes that fit perfectly into a square. Since its discovery, the underlying structure of the puzzle has...

Mural Mathematics

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Topic(s):

Geometry, Mathematical Modeling, Social Justice Mathematics

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Facilitator Guides, Handouts, Photos & Videos

Students will explore existing equity themed murals to identify themes, and the mathematics necessary to plan/create a city mural. Students will utilize Google maps tools to begin connecting Mathematical representations to precisely interpret circle properties and apply them to the mural design.

Fold & Cut

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Topic(s):

Geometry, Problem Solving / General

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Handouts, Photos & Videos, References, Virtual Tools

What shapes can result from the following fold-and-cut process?
Take a piece of paper.
Fold it flat.
Make one complete straight cut.
Unfold the pieces.
Are all shapes possible?

Making Connections Between Forms of Quadratic Equations

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Mary Beth Richey

Topic(s):

Geometry

Supporting Resources:

Facilitator Guides, Handouts, Virtual Tools

Developed as part of the Math Circles of Inquiry project, the goal of this module is to help students in Algebra II become fluent in the various forms of a parabola equation based on the information that they are given. Students sometimes fail to understand that there are multiple ways...

Trigonometric Ratios in Right Triangles

By:

Mary Beth Richey, Mary Plumb

Topic(s):

Geometry

Supporting Resources:

Facilitator Guides, Handouts, Lesson Plan

Developed as part of the Math Circles of Inquiry project, this five to six day activity is designed to help students understand trigonometric ratios, by building on their understanding of similar triangles and ratios of corresponding sides. The purpose of this module is for students to spend time and energy...

Systems of Linear Equations

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Alexandra Edwards, Dyan Palmer, Ryan Gantner

Topic(s):

Algebra / Arithmetic, Geometry

Supporting Resources:

Facilitator Guides, Handouts

Developed as part of the Math Circles of Inquiry project, this short module explores a graphical solution to a system of equations. Students answer questions about lemonade sales and physically stand on the coordinates of a giant grid in order to see that plotting two equations on the same set...

System of Inequalities: Math Dance

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Alicia Pakusch, Rachel Pellegrino

Topic(s):

Algebra / Arithmetic, Geometry

Supporting Resources:

Facilitator Guides, Handouts, Lesson Plan

You want this year’s dance to be LIT! The dance committee has a goal of fundraising $3,500 through ticket sales. How many tickets do they need to sell? Developed as part of the Math Circles of Inquiry project, this module presents an engaging problem which will allow students to investigate...

Optimal Locations of Firehouses (Taxi-cab Metric)

By:

Joshua M. Sabloff

Topic(s):

Algebra / Arithmetic, Geometry, Problem Solving / General

Supporting Resources:

Facilitator Guides

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...

Pigeonhole Principle and Parity Problems

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Brian Conrey, Corinne Cristiani

Topic(s):

Algebra / Arithmetic, Combinatorics, Geometry, Number Theory, Parity / Invariants, Problem Solving / General

Supporting Resources:

Facilitator Guides

The pigeonhole principle states that if n pigeons are put into m cubbies, with n > m, then at least one cubby must contain more than one pigeon. Parity problems deal with odd and even integers. Here is a collection of problems that can be used in a single problem...

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...

Topic: Geometry