Postulates!
The 4th Postulate says:
All right angles are CONGRUENT
Name something impossible to have on the surface of a sphere
Parallel Lines, straight lines
Draw a triangle affected by Hyperbolic Geometry
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If you drew a sphere on a flat, spherical, and hyperbolic surface, which would have the greatest circumference?
Hyperbolic
Define, "Local Extrema"
A Maximum or Minimum in a certain area on a graph
Is the third postulate broken by spherical geometry?
You cannot draw a 'circle' on the surface of a sphere, so yes.
What type of circle does not touch both poles on a sphere?
What type of circle does touch both poles on a sphere?
Small circle, Great circle
Hyperbolic geometry has more __________________________ than Euclidean OR spherical geometry.
Non-intersecting lines
Who wrote the Sin-TAAD rule?
Napier
Draw roughly what I'd get if I graphed -x2
n
Come up with a way to break/disprove the 1st postulate.
Draw the points on a curved surface. The fastest path is no longer a straight line.
A sphere has ______________________________________
Constant positive curvature
A hyperboloid has _____________________________________
Constant negative curvature
What is the sin-TAAD rule?
A spherical triangle can have anywhere from 0, 1, 2, or 3 right angles
You can find these postulates where?
In the beginning of The Elements
If you draw a triangle on the surface of a sphere, the angle measures will add up to between ______ and ______.
180* and 540*
What is a limited parallel?
The closest line possible to a parallel line
What do you call a geometric shape with more than 2 sides drawn on a sphere?
A spherical polygon
Take the integral of '15'
15x
Define the 5th Postulate, and be accurate.
If two lines intersect a third, and the sum of the inner angles is less than 180*, then those lines will intersect
What do you call a triangle that has less or more than one right angle on the surface of a sphere?
A spherical oblique triangle
What did Johann Gauss discover, and what is it?
Define lines of latitude and longitude in terms of Great and Small Circles.
Longitude: Great Circles
Latitude: small circles
What are the zeros of the following function:
y = (x+3)(x-2)
-3, +2