Oakland East Bay Math Circle NonEuclidean Geometry Worksheet by langstonwalker

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									      Oakland
East
Bay
Math
Circle:
Non­Euclidean
Geometry
Worksheet



Using
the
rubber
bands
and
spheres
you
have,
follow
the
instructions
below
to
test

the
rules
of
geometry.

Remember
that
in
elliptic
geometry,
a
“straight
line”
is
really

a
great
circle
(a
circle
that
has
the
same
diameter
of
the
sphere
it’s
on).





1.
 Use
three
rubber
bands
to
create
different
triangles
on
the
sphere.

Make
four

    different
triangles
and
use
your
protractor
to
measure
all
three
angles
inside
the

    triangle.

Try
to
make
very
different
triangles.

Write
the
angles
below.






        Triangle
1:
 __________
      __________
      __________








        Triangle
2:
 __________
      __________
      __________








        Triangle
3:
 __________
      __________
      __________








        Triangle
4:
 __________
      __________
      __________





2.
 For
each
of
the
triangles
you
made,
find
the
sum
of
the
angles
on
the
inside
of
the

    triangle.






        Triangle
1:
 __________



+
 __________



+
 __________



=
 __________








        Triangle
2:
 __________



+
 __________



+
 __________



=
 __________








        Triangle
3:
 __________



+
 __________



+
 __________



=
 __________








        Triangle
4:
 __________



+
 __________



+
 __________



=
 __________





3.
 Are
the
sums
of
the
angles
of
the
triangle
180
degrees?



4.
 Now
use
the
rubber
bands
to
make
three
different
right
triangles.
Use
the

    measuring
tape
to
measure
the
lengths
of
the
three
sides
in
millimeters,
and
write

    them
below.








        Triangle
1:
 __________




 __________




 __________











        Triangle
2:
 __________




 __________




 __________








5.
 Do
these
sides
satisfy
the
Pythagorean
theorem?




 
      (First
smallest
side)2
+
(Second
smallest
side)2
=
(Hypotenuse)2








        Triangle
1:
 (__________)2
+
 (__________)2
=
 (__________)2








        Triangle
2:
 (__________)2
+
 (__________)2
=
 (__________)2





6.
 What’s
different
between
the
geometry
we’re
used
to
(Euclidean
geometry)
and

    the
geometry
on
a
sphere
(Elliptic
geometry)
that
might
account
for
these

    differences?


								
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