GBK Geometry * 2009-10

Report
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!

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