Download Spherical Geometry Notes

Spherical Geometry
No.
1
2
Euclidian Fact
Two points
determine a line.
Name________________________
Picture
Spherical Fact
B
A
2 lines intersect at
one point and form
4 angles.
1
2
3
4
3
3
4
5
6
7
8
Through a point not
on a line there
exists one parallel
line.
Perpendicular lines
form 4 right angles.
3 non-collinear
points form a
triangle.
Triangle sum is
1800.
A triangle can have
(at most) one right
or one obtuse angle.
1
2
3
3
Each angle of an
equiangular triangle
measures 600.
Some extra spheres and anything else you want to remember:
Page 1 of 2
Picture
6 7
1
2
3 45
9
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10
11
12
13
1. Honolulu (HNL)
4. Miami (MIA)
7. Paris (CDG)
10. Bangkok (BKK)
Page 2 of 2
2. Los Angles (LAX)
5. New York (JFK)
8. Milan (MXP)
11. Singapore (SIN)
13. Sydney (SYD)
3. Dallas (DFW)
6. London (LHR)
9. Moscow (DME)
12. Philippines (MNL)
Spherical Geometry - Answers
No.
1
2
3
4
5
6
Euclidian Fact
Two points
determine a line
Picture
Spherical Fact
A great circle
forms a line
B
A
2 lines intersect at
one point (and form
4 angles)
Through a point not
on a line there
exists one parallel
line
2
1
4
3
P
2 lines intersect at
two points(and
form 8 angles)
Perpendicular lines
intersect twice and
form 8 right angles
3 non-collinear
points form a
triangle
3 non-collinear
points form a
triangle
1
2
3
Triangle sum is
greater than 180
and less than 540
7
A triangle can have
one obtuse angle
(one right angle)
A triangle can have
more than one
obtuse angle (one
right angle)
8
Each angle measure
of an equiangular
triangle is 60.
Each angle measure
of an equiangular
triangle can vary.
Some extra spheres and anything else you want to remember:
Page 3 of 2
A
B
1 2
4 3
5
6
8
7
No parallel lines
exist in spherical
geometry
Perpendicular lines
form 4 right angles
Triangle sum is
1800.
Picture
5
6
8
7
1 2
4
3
B
A
C