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The Geometer's Sketchpad Activities
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.
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.
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.
Using problem solving skills, formal geometry, and The Geometer’s
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.
Using problem solving skills, formal geometry, and The Geometer’s
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.
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.
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.
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.
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.
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.
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.
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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