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11 Cards in this Set
- Front
- Back
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1st axiom of Euclid |
Through any 2 points passes a unique line |
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2nd axiom of Euclid |
It is possible to extend any line segment into a straight line |
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3rd axiom of Euclid |
It is always possible to draw a unique circle of any radius around a given point |
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4th axiom of Euclid |
All right angles are equal |
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5th axiom of Euclid/parallel postulate |
If a straight line crossing 2 straight lines makes interior angles on the same side whose sum is less than 2 right angles, the two lines will intersect if drawn indefinitely |
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Distance (coordinate geom) |
Pythagoras theorem |
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Distance between p1 and p2 (metric geom) |
Use a abstract function (coordinates to positive reals). There are many different possible functions |
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Distance between p1 and p2 (Geometric) |
There exists a unique line between any two points (A1). Define a unit length then set the line between two points to be the positive real numbers. Then p1 is set to be 0, and p2 is d the length. |
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Definition of Euclid's right angle |
If a straight line intersects another straight line s.t. 2 angles on the same side are equal. Then these equal angles are right angles. |
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Rigorous procedure to measure angle ABC |
Create a circle (center B) around the angles and extend the lines (AB and BC) till they intersect (call these points A',C'). Then map circumference of the circle to the number line 0 to tau. The angle is the length of line A'C' (anticlockwise). |
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Angle rules |
Angle ABC = tau - Angle CBA Angle ABC + Angle CBA = tau A right angle is pi/2 A flat angle is pi |
