Title: Geometry Applications: Geometry Basics: Circles

Title: Geometry Applications: Geometry Basics: Circles

[Music]

[Music]

IN CHOCO CANYON, NEW MEXICO

THE PUEBLO INDIANS BUILT AN ELABORATE VILLAGE

IN THE MIDST OF THE DESERT.

THE SPANISH REFERRED TO IT AS PUEBLO BONITO,

WHICH MEANS "PRETTY VILLAGE".

BUT BY THE TIME THE SPANIARDS SAW IT

IT WAS ALREADY THE ABANDONED SET OF RUINS

THAT SURVIVE TO THIS DAY.

BUT THE DESERT DOESN'T HIDE EVERYTHING.

SEEN FROM ABOVE, THIS PUEBLO VILLAGE

REVEALS A NUMBER OF CIRCULAR STRUCTURES.

THE PUEBLO INDIANS REFER TO THEM AS KIVAS,

SACRED PLACES WHERE CEREMONIAL RITUALS TOOK PLACE.

WHY A CIRCULAR STRUCTURE?

CIRCLES HAVE CULTURAL MEANING

IN THAT THEY REFER TO THE CYCLES OF NATURE.

IN PARTICULAR, FOUR NATURALLY RECURRING

CELESTIAL EVENTS WERE OF IMPORTANCE

TO ANCIENT CULTURES.

THE WINTER SOLSTICE, WHEN THE EARTH'S AXIS IS TILTED

FARTHEST AWAY FROM THE SUN; THE SUMMER SOLSTICE,

WHEN THE EARTH'S AXIS IS TILTED CLOSEST TO THE SUN;

THE FALL EQUINOX, WHEN THE EARTH'S AXIS IS NOT

TILTED IN ANY DIRECTION AWAY OR TOWARD THE SUN.

DAY AND NIGHT ARE EQUAL IN LENGTH, BUT AFTER THIS POINT

THE DAYS BECOME SHORTER IN LENGTH

WHILE NIGHT TIME IS LONGER.

THE SPRING EQUINOX, LIKE THE FALL EQUINOX,

DAY AND NIGHT ARE EQUAL IN LENGTH,

BUT AFTER THIS POINT THE DAYS BECOME LONGER.

THIS ANNUAL CYCLE IS REPRESENTED BY THE

CIRCULAR SHAPE OF THE KIVA.

AND THE PUEBLO, LIKE MANY ANCIENT CULTURES,

WERE INTERESTED IN IDENTIFYING

THESE IMPORTANT EVENTS.

THE LOCATION OF THE SUN ON THE HORIZON IS AN INDICATOR

OF EACH OF THESE FOUR SEASONAL CHANGES.

PUEBLO BONITO WAS BUILT IN SUCH A WAY TO HIGHLIGHT

WHEN THESE SEASONAL CHANGES OCCURRED.

THE ALIGNMENT OF SHADOWS CREATED BY THE SUN

WAS THE BEST INDICATOR OF THE SOLSTICE OR EQUINOX.

CIRCULAR STRUCTURES ARE IDEAL FOR

TRACKING THESE ASTRONOMICAL CHANGES.

FOR EXAMPLE, THE ARRANGEMENT OF ROCKS AT STONEHENGE

IN ENGLAND IS MEANT TO ALIGN WITH THE SOLSTICES

AND EQUINOXES IN SUCH A WAY THAT

THE SUN APPEARS BETWEEN THE MASSIVE STONES.

WHENEVER YOU'RE ON THE EARTH'S SURFACE

YOUR POSITION MARKS OUT A CIRCULAR LINE OF SIGHT

TO THE HORIZON.

YOUR POSITION IS AT THE CENTER OF THE CIRCLE.

THE POSITION OF THE SUN ON THE HORIZON

FORMS A RADIUS OF THE CIRCLE.

THE VARIOUS POSITIONS ON THE HORIZON

FOR THE VARIOUS SOLSTICES AND EQUINOXES

FORM DIFFERENT RADII WITH THE CENTER OF THE CIRCLE.

FINALLY, THE SEGMENTS CONNECTING THESE

VARIOUS POSITIONS OF THE SUN

FORM CHORDS THAT DEFINE INTERCEPTED ARCS.

WHETHER A KIVA OR AN OBSERVATORY, CIRCULAR

STRUCTURES ARE IDEAL FOR STUDYING THE NIGHT SKY.

TAKING ADVANTAGE OF THE GEOMETRY OF CIRCLES,

THESE STRUCTURES HAVE DEGREES OF FREEDOM

THAT OTHER STRUCTURES DON'T HAVE.

IN THIS PROGRAM YOU'LL SEE HOW CIRCLES

HAVE BEEN USED TO SOLVE REAL WORLD PROBLEMS

AS WELL AS CERTAIN DESIGN CHALLENGES.

IN PARTICULAR, THIS PROGRAM WILL COVER

THE FOLLOWING KEY CONCEPTS