Download Geometry in the Real World

Geometry in the Real World
JENNIFER TOURGEE
SECOND HOUR HONORS GEOMETRY
O C T O B E R 4 TH, 2 0 1 1
Points
POINTS ARE ONE OF THE THREE UNDEFINED
TERMS IN GEOMETRY. THEY ARE USED TO
SHOW THE LOCATION OF SOMETHING. THE
LOCATION IS DEFINED BY ITS
COORDINATES.
The green dot is
used to show the
point of the center
of the Earth. It is
used for emphasis.
The actual point of
the exact center has
no size.
EXAMPLES
OF POINTS
 The exact center of
the Earth is a point.
 Another point is the
exact location where
two walls and a ceiling
meet.
Again, the point
where the ceiling
and walls meet has
no size. It is just
used to show the
point of
intersection.
Lines
LINES ARE THE SECOND UNDEFINED TERM
IN GEOMETRY. THEY CAN BE USED TO
CONNECT NODES IN A NETWORK AND HAVE
NO THICKNESS OR WIDTH.
EXAMPLES
OF LINES
 An example of a line
is the metal rails of a
railroad track.
 Also, the line in
which a bullet travels
when fired is a line,
because it can go on for
a long time until either
gravity takes over or
the bullet hits
something.
Railroad tracks seem to
go on forever in two
directions, if standing in
the middle and nowhere
near the end of the line.
They are parallel and
never intersect.
Planes
PLANES ARE THE THIRD UNDEFINED TERM
IN EUCLIDEAN GEOMETRY. THEY ARE TWODIMENSIONAL SURFACES IN WHICH A
STRAIGHT LINE BETWEEN TWO POINTS WILL
LIE WHOLLY ON THAT SURFACE.
The white outline on
the computer screen
shows the edge of the
plane.
EXAMPLES
OF PLANES
 A flat computer
screen is a plane.
 Doors without the
handle could be
considered planes.
Without the handle ,
windows, and
knocker, this door is
a plane.
Line Segments
LINE SEGMENTS ARE PARTS OF LINES CUT
OFF BY TWO END POINTS.
EXAMPLES
OF LINE
SEGMENTS
 Piano keys are line
segments because they
begin at one point and
end at another.
 The heads of tennis
rackets have line
segments across them,
both horizontally and
vertically.
Angles
ANGLES ARE THE SPACES BETWEEN TWO
LINES OR THREE OR MORE PLANES
DIVERGING FROM A COMMON POINT, OR
WITHIN TWO PLANES DIVERGING FROM A
COMMON LINE.
EXAMPLES
OF ANGLES
 The space between
the hour and minute
hands of the clock is an
angle.
 Another angle that is
found in the real world
is the right angle on a
cardboard box.
Rays
RAYS ARE LINES THAT HAVE ONE ENDPOINT
AND GO ON FOREVER IN THE OTHER
DIRECTION.
EXAMPLES
OF RAYS
 The light from a
flashlight starts at one
point and can go on
forever until it hits
something else.
 Radio waves could be
considered rays because
they can go on till
almost forever.
Circles
A CIRCLE IS A ROUND PLANE FIGURE WHOSE
BOUNDARY (CIRCUMFERENCE) CONSISTS OF
POINTS EQUIDISTANT FROM A FIXED
CENTER.
EXAMPLES
OF CIRCLES
 Pizzas are circles. If
the pizza was cut into
equal slices, the slices
would be considered
sectors of the pizza.
 Tires are circles.
SECTOR
Midpoints
A MIDPOINT IS A POINT THAT IS IN THE
MIDDLE OR EQUIDISTANT FROM EACH END
OF THE LINE.
EXAMPLES
OF
MIDPOINTS
 A ruler has a
midpoint of six.
A football field has its
Midpoint
midpoint at the fifty
yard line.
Midpoint
Networks
A NETWORK IS A SET OF NODES THAT ARE
CONNECTED BY ARCS.
EXAMPLES
OF
NETWORKS
Stream network
 An example of a
network is a bunch of
smaller streams
merging into a large
stream.
 Another example is
power lines carrying
electricity.
Power lines
Polygons
A POLYGON IS A CLOSED PLANE FIGURE
HAVING THREE OR MORE (AND USUALLY
STRAIGHT) SIDES.
EXAMPLES
OF POLYGONS
 Legos are a variety of
shapes, many of them
polygons.
 iPods are polygons.
They are normally
squares or rectangles.