## Virtual Math Trail

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This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

# Virtual Math Trail

Welcome to the Virtual Architectural Math Trail!

Math trails were created in Australia as a way to relate math to real life situations.

We'll  follow a virtual trail from the Museum Campus of Chicago along the lake front to Navy Pier and then to North Michigan Avenue and back to the Chicago River.  Along the route we'll view five structures and see a geometry concept in use (not just an concept on the page of a math book).

The trail begins at the Field Museum of Natural History (http://fieldmuseum.org/)  located at Lake shore Drive and E. Roosevelt Road.  It was built in 1909-1912 and designed by D. H. Burnham and Company.  The Field Museum is patterned after the Erechtheium, one of the temples on the Acropolis.

The triangular shape over the entrance is called a pediment.  Triangles may be classified two ways:  by the length of their sides and by their angles.  http://homepage.mac.com/efithian/Geometry/Activity-04.html

What are the two classifications for the pediment?

Traveling north on Lake Shore Drive to Navy Pier.  When it was built in 1916, Navy Pier was the world's largest pier. No longer is used for commercial shipping, it was renovated in 1995 as a tourist attraction.  One of the new features is a Ferris wheel.  It stands 150 feet high (100 feet shorter than the first Ferris wheel at the 1893 Columbian Exposition in Chicago!)

The diameter of the Ferris wheel is 140 feet.   What is the circumference of the Ferris wheel?  What is its area?  http://www.sisweb.com/math/geometry/circles.htm

Moving east from Navy Pier to North Michigan Avenue.  At the southwest corner of Erie St. and North Michigan Avenue is the Crate and Barrel store.  It was designed by Solomon Cordwell Buenz and Associates and built in 1990.

What two solid shapes are used in the design of the building ( http://homepage.mac.com/efithian/Geometry/Activity-04.html) ?

(Why do you think that the architects chose these solid figures for this store)

Is the design symmetrical?  Why or why not?

Move south along North Michigan Avenue to Wacker Drive along the south bank of the Chicago River. Move west to State Street.  Across the river is Marina City, twin sixty story towers.  It was built in 1959 and was designed by Bertrand Goldberg Associates.

The two towers have the shape of what solid figure ( http://homepage.mac.com/efithian/Geometry/Activity-04.html)?   If each floor is about 10 feet high, what is the approximate height of each tower?

Four blocks west of Marina City is the Merchandise Mart.  It was built in 1930 from plans by Graham, Anderson, Probst, and White.  At 25 stories high and covering two city blocks, it is the largest commercial building in the world.

Look at the facade of the building facing the river.  Where is the line of symmetry ( http://www.harcourtschool.com/activity/elab2002/grade_4/019.html) ? List two architectural features (number of windows, etc.) that are mirror images of each other?

This is the end of this virtual math trail.  If you have the opportunity to actually walk the trail, look for other geometry concepts along the way.

What are the two classifications for the pediment?   It is an isosceles triangle and an obtuse triangle

What is the circumference of the Ferris wheel? The circumference is 439.6 ft.

What is its area? The area is 15,386 ft2

What two solid shapes are used in the design of the building? The corner is a cylinder.  The rest of the building is made of rectangular prisms.

(Why do you think that the architects chose these solid figures for this store?)  The cylinder represents the barrel, and the rectangular prisms are the crates.

Is the design symmetrical? No  Why or why not? There is no line of symmetry either horizontal or vertical.  Neither half of the building is the mirror image of the other half.

The two towers have the shape of what solid figure?  The towers are basically both cylinders.

If each floor is about 10 feet high, what is the approximate height of each tower? There are 60 floors so 60 x 10 = 600 feet.  The actual height is 587 feet.

Look at the facade of the building facing the river.  Where is the line of symmetry? The line of symmetry runs vertically through the center.

List two architectural features (number of windows, etc.) that are mirror images of each other?  At the first floor, there are twelve window bays on either side of the center door.  The two towers on either side are mirror images of each other.  The roofline forms an isosceles triangle.