Maps and Math: Using maps to enrich tasks David Sabol | Saint Ignatius High School in Cleveland, Ohio tweeters: @dave_sabol
Jan 15, 2015
Maps and Math: Using maps to enrich tasksDavid Sabol | Saint Ignatius High School in Cleveland, Ohiotweeters: @dave_sabol
Thales of Miletusc. 620-546 BCE!
“Western philosophy began with Thales.” – Bertrand Russell
Thales measures the pyramids http://projectionsystems.wordpress.com/
-Plutarch
“…without trouble or the assistance of any instrument [Thales] merely set up a stick at the
extremity of the shadow cast by the pyramid and, having thus made two triangles by the impact of
the sun’s rays, … showed that the pyramid has to the stick the same ratio which the shadow [of the
pyramid] has to the shadow [of the stick].”
Thales measures the pyramids http://projectionsystems.wordpress.com/
Main Building TowerConstructed in 1891
…from GeoGebra… Tower shadow (on science building): 4.28 Science building shadow: 1.6 Goal post shadow: 1.04 Goal post height: 30 feet
…from GeoGebra… Tower shadow (on science building): 4.28 Science building shadow: 1.6 Goal post shadow: 1.04 Goal post height: 30 feet
301.04
= x1.6 + 4.28
x ≈169.62
Main Building TowerConstructed in 1891
Tower Height: 159 feet Error: approx 6.3%
Not bad. !
Maybe? !
What could we have done to make it better?
Tips
• Look around
• Bing
• Yahoo
• ???
• Find creative sources for the reference.
• Try to find an object you can measure several ways.
What say you, Youngstown?
Closest team credit: Deadspin
Most liked team per county credit: Facebook
Media markets credit: Facebook
Voronoi DiagramsNamed after Georgy Voronoy1868-1908
source: wikipedia
source: jasondavies.com
source: jasondavies.com
source: Reddit.com user asbusinessmagnet
Zooming and Dilation
Factor ≈ 0.7009
Factor ≈ 0.7148
Factor ≈ 0.6995
Factor ≈ 0.4783
Factor ≈ 0.4831
Factor ≈ 0.5171
Factor ≈ 0.4872
Factor ≈ 0.4278
Factor ≈ 0.4448
Zoom Level Factor
1 -2 0.70093 0.71484 0.69955 0.47836 0.48317 0.51718 0.48729 0.4278
10 0.4448
Zoom Factors
Speed Trap Let’s watch.
Any questions?
approx 123 feet
Speed Trap Let’s get some speeders.
Car ∆d ∆t AROC
Red sedan 123 ft 3.37 sec
Black SUV 123 ft 3.17 sec
Red truck 123 ft 3.30 sec
Grey sedan 123 ft 2.97 sec
Car ∆d ∆t AROC
Red sedan 123 ft 3.37 sec 24.89 mph
Black SUV 123 ft 3.17 sec 26.45 mph
Red truck 123 ft 3.30 sec 25.41 mph
Grey sedan 123 ft 2.97 sec 28.23 mph
So how long would the trip take if they weren’t speeding? Anyone?
123 feet 15 mph
Some nice maps sites• http://www.jonathancrowe.net/maps/
• Strange maps: http://bigthink.com/blogs/strange-maps
• http://www.reddit.com/r/maps
Maps and Math: Using maps to enrich tasksDavid Sabol | Saint Ignatius High School in Cleveland, Ohiotweeters: @dave_sabol