GBK Geometry * 2009-10
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Transcript GBK Geometry * 2009-10
GBK GEOMETRY – 2012-13
Jordan Johnson
Week One, Day Two
TODAY’S AGENDA
Greetings
Syllabus signatures? (~1 min)
Review Rules (~5 min)
Euclid, Constructions, and Equilateral Triangles
(~10 min)
First Geometric Construction (~10 min)
GeoGebra demo (~10 min)
Homework / Questions (~5 min)
Clean-up
YESTERDAY’S WORK: RESPECT
In 5 minutes, answer this question in as many
ways as possible:
What does “respect” mean, and how can we
demonstrate respect here?
Now: For each of those two questions, choose the
three answers that seem most important to you
as a group.
Be ready to share your results.
RULES
Now consider the second question:
How can we demonstrate respect here?
Choose one answer to the second question that
seems most important to you as a group.
Goal: simple rules that say what we do want to
see in class at all times.
Each group: produce one card with a rule, from
one of your ideas.
EUCLID & ALEXANDRIA
EUCLID’S ELEMENTS
CONSTRUCTIONS &
EQUILATERAL TRIANGLES
Equilateral triangle: one
whose sides are all of equal
length (and angles are all of
equal size)
Task:
Draw a line segment of length
12cm using your ruler; label its
ends A and B.
Set your compass to the length
of the segment, and draw an arc
centered at A, then another arc
centered at B.
Label the intersection point C.
Bonus: If that was
really easy, try a regular
hexagon (i.e., one whose
sides are all equal).
CONSTRUCTIONS &
EQUILATERAL TRIANGLES
This was a construction: a figure designed to
satisfy given conditions.
(In this case: all sides are of equal length.)
“Construct” usually means using a compass and
a straightedge.
THE SURFER’S & SPOTTER’S PUZZLES
Spotter: Wants access to all
corners
Surfer: Wants
access to all sides
THE ISLAND
Equilateral triangular
island
12km on each side
THE SPOTTER
Goal:
Choose a location for his house
Minimize the sum of the distances from the house to
the vertices A, B, and C.
THE SPOTTER
Scale drawing of the
island: 1cm = 1km
Example 1:
House at D
AD = 4.4km, DB = 9.1km,
DC = 7.9km
Total distance: 21.4km
Example 2:
House at E
AE = 10.4km, EB = 5.1km,
EC = 6.9km
Total distance: 22.4km.
THE SPOTTER
Using your triangle from yesterday or a new one
(12cm on each side) as a model:
Choose several points on the island
For each point:
Measure the distance to each corner
Add up the distances.
What do you believe is the best place for the
house?
…and how many km of path must the spotter clear?
What about the worst place?
…and how many km to clear from there?
HOMEWORK
Same homework as yesterday:
your bio / introduction email. Due Friday.
Posted online at the course Web site.
Tomorrow:
Bring your supplies (compass, ruler, notebooks,
protractor).
Bring your signed syllabus form.
CLEAN-UP / REMINDERS
Pick up all trash / items.
Put all borrowed items back in place.
Push in chairs (at front and side tables).
See you tomorrow!