OAME Geometry Ideas
Aanii, Bonjour, Hello!
We here in the Durham Region, respectfully acknowledge that we are on the traditional lands of the Mississaugas of Scugog Island.
What Do You Notice and Wonder?
A Concrete-Diagrammatic-Symbolic Approach
Circle Properties: A C-D-S Approach
Circle Properties: A C-D-S Approach
Find the Middle of the Wooden Circle
Triangle Properties
4 cm
12 cm
4 cm
Triangle Properties: Side Lengths
Triangle Properties: Side Lengths
‘Shortest’ | ‘Middle’ | ‘Longest’ |
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Triangle Properties
Triangle Properties
Interlude: What do Angles Measure?
Angles measure turn.
Triangle Properties: Angles
Length a | Length b | Length c | Angle A | Angle B | Angle C |
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A
C
B
a
b
c
>>start with a scalene triangle
Impossible Triangles
Only one of these triangles is possible: which one?
110˚
25˚
3 cm
3 cm
20˚
130˚
5 cm
4 cm
3 cm
6 cm
2 cm
4 cm
7 cm
8 cm
30˚
60˚
6 cm
3 cm
Coding Challenge
‘Pythagoras’ Theorem
>>> Math as the global endeavour… it belongs to all of us
Sum of Three Squares Non-Right Triangles
Connections to the Number Line
A Key Skill: Decomposing and Recomposing
A Key Skill: Decomposing and Recomposing
What is the area of this semi-circle?
Source: Catriona Agg @CShearer41
Analysing Designs: Kolam Art
Source: Getty Images
Analysing Designs: Islamic Geometric Art
Source: Wikimedia Commons
Analysing Designs: African Fractals
Analysing Designs: a Recent Breakthrough
Periodic Tilings with a Single Tile
It was already known that we could use a single tile (like a triangle or a quadrilateral) to tile the plane in a periodic way...
Aperiodic Tiling with Two Tiles
And Roger Penrose showed that you could use two tiles to tile the plane in an aperiodic way...
Aperiodic Tiling with One Tile
This is an incredible discovery from Craig Kaplan (from the University of Waterloo), David Smith, Joseph Myers and Chaim Goodman-Strauss proves that a single tile (called "the hat”) will cover a plane in an aperiodic way.
Geometry: a Global Endeavour
Hawaiki Rising by Sam Low (University of Hawaii Press)
Geometry: a Global Endeavour
Geometry: a Global Endeavour
Telling Time and Finding Latitude
Sources: https://www.lessonsfromearthandbeyond.ca/lessons-from-beyond.html
https://skyandtelescope.org/astronomy-resources/make-a-star-clock/
Tristan Gooley: The Natural Navigator
How Many Minutes to Sunset?