maps and math cwic

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