Title: Geometry Applications: Geometry Basics: Polygons
Title: Geometry Applications: Geometry Basics: Polygons
[Music]
[Music]
THE WORLD'S MOST FAMOUS OFFICE BUILDING,
THE PENTAGON, WAS ORIGINALLY
MEANT TO BE LOCATED ELSEWHERE.
DURING WORLD WAR II THIS BUILDING WAS TO BE
BUILT ACROSS FROM THE LINCOLN MEMORIAL
AND NEAR ARLINGTON MEMORIAL CEMETERY.
IN FACT, SOME FARMLAND HAD BEEN CHOSEN
AND IT HAPPENED TO BE IN THE SHAPE OF A PENTAGON.
NOT AN EVEN SIDED REGULAR PENTAGON,
BUT A PENTAGON NONETHELESS.
FOR SIMPLICITY THE ARCHITECTS DECIDED TO
MAKE THE OFFICE BUILDING IN THE SHAPE OF THE FARMLAND.
BUT PROBLEMS EMERGED WHEN IT BECAME APPARENT
THAT THE PROPOSED LOCATION OF THE NEW OFFICE BUILDING
WOULD INTERFERE WITH THE VIEW OF ARLINGTON CEMETERY
WHEN SEEN FROM THE WASHINGTON SIDE OF
THE POTOMAC RIVER.
A DECISION WAS QUICKLY MADE TO RELOCATE THE BUILDING
FARTHER DOWN THE RIVER.
THE DEMANDS OF WARTIME PREVENTED
AN ENTIRELY NEW BLUEPRINT FOR THE OFFICE BUILDING.
BUT THE ARCHITECTS DID MAKE ONE SIGNIFICANT CHANGE.
THE BUILDING WOULD BE A REGULAR PENTAGON
AND THUS THE PENTAGON, AS THE BUILDING
HAS SINCE COME TO BE KNOWN, CAME TO BE.
IN THEIR RUSH TO CREATE THE NEW OFFICE BUILDING,
THE DESIGNERS CAME UP WITH A BUILDING
WHOSE SHAPE OFFERS SOME CLEAR ADVANTAGES.
LET'S COMPARE A SQUARE
INSCRIBED IN A CIRCLE OF RADIUS R
TO A REGULAR PENTAGON INSCRIBED IN THE SAME CIRCLE.
THE INCREASE IN THE NUMBER OF SIDES FOR THE PENTAGON
RESULTS IN A SIZABLE INCREASE IN THE PERIMETER.
THIS IS IMPORTANT FOR A BUILDING THAT NEEDED
A HUGE NUMBER OF OFFICE SUITES.
FURTHERMORE, THE FIVE SIDES
OFFER MORE ANGLES OF APPROACH
FOR THE SURROUNDING ROADS AND HIGHWAYS.
THIS EXAMPLE ILLUSTRATES THE VERSATILITY OF POLYGONS.
WITH AN INCREASE IN THE NUMBER OF SIDES
COME OTHER PROPERTIES THAT MAKE POLYGONS
THE SOLUTION TO CERTAIN DESIGN PROBLEMS.
IN THIS PROGRAM YOU WILL EXPLORE SOME REAL WORLD
PROBLEMS THAT INVOLVE THE USE OF POLYGONS.
SPECIFICALLY, THIS PROGRAM WILL ADDRESS
THE FOLLOWING CONCEPTS:
THE FOLLOWING CONCEPTS: