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The Geometer's Sketchpad Activities

Exploring Characteristics of Triangles

Students draw triangles and explore the classification of each using the measures of interior angles and lengths of sides. In the extension activities, the students further explore and generalize a formula for the sum of the interior angles of convex polygons.

Constructions of Isosceles and Equilateral Triangles

Students discuss the difference between drawing and constructing a triangle using The Geometer's Sketchpad. They will further develop constructions for both isosceles and equilateral triangles. In the extension activities, students will script the construction of a right triangle.

The Pythagorean Theorem

Students create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. These demonstrations are based on proofs by Bhaskara, Leonardo da Vinci, and Euclid. Students will value this activity more if they have already had some experience with the Pythagorean Theorem.

Exploring Centers of a Triangle: Part 1

Using problem solving skills, formal geometry, and The Geometerís Sketchpad, students will model and solve two real-world problems by constructing the incenter and circumcenter of triangles. Students will further explore relationships between the angle and side bisectors of arbitrary triangles. The author wishes to acknowledge Dr. Billie F. Risacher for providing the real-world scenarios.

Exploring Centers of a Triangle: Part 2

Using problem solving skills, formal geometry, and The Geometerís Sketchpad, students will model and solve a real-world problem by constructing the centroid of a triangle. Students will explore further relationships of the medians of a triangle and investigate how the centroid partitions each of the medians.

Determining the Uniqueness of a Circle

Are there a certain number of arbitrary points, such that there exists a unique circle through them? To explore and conjecture an answer to this question, students will construct circles passing through various numbers of given points. This activity was adapted from an activity developed by Sean Jones, a fourth-year pre-service teacher at the University of Virginia in Spring 1998.

Exploring and Creating Tessellations

Students explore and construct several different types of tessellations. The first part of the activity uses only regular polygons to create pure and semi-pure tessellations; therefore, you will need pre-recorded scripts for the construction of an equilateral triangle, a square, and a regular hexagon. The second part of the activity extends the notion of tessellations to create non-regular polygon and "Escher-like" tessellations.

Exploring Geometric Constructions of Parabolas

This activity is an introduction to geometric constructions of parabolas. Students investigate the properties and characteristics of parabolas. This activity has been adapted from the following article: Olmstead, E.A. (1998). Exploring the locus definition of the conic sections. Mathematics Teacher, 91(5), 428-434.

Exploring the Witch of Agnesi

Students construct the graph of the Witch of Agnesi, and investigate both its asymptotes and inflection points. Fermat studied this function in the seventeenth century. Students are introduced to the animate features of The Geometer's Sketchpad.

Exploring Infinite Series through Baravelle Spirals

This activity is an introduction to the concept of convergent infinite series using a recursive geometric construction. This activity has been adapted from the following article: Choppin, J. M. (1994). Spiral through recursion. Mathematics Teacher, 87(7), 504-508.

Exploring the Golden Rectangle

Students will construct a golden section and a golden rectangle and study their characteristics and connections with the Fibonacci series. They will import pictures from the internet and download them into the Sketchpad. Using their "golden" construction, they will discover the use of the golden rectangle in famous works of art. This exploration was adapted from an activity developed by Elizabeth Boiardi while she was a graduate student at the University of Virginia in the summer of 1998.

Exploring Trigonometric Functions

Students geometrically construct and investigate the graphs of sine and cosine based upon the lengths of the sides of a reference triangle.

Send comments or questions to Beth Cory at blc4j@virginia.edu.

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Last modified on January 2, 2002.