The search for new Mathematical axioms
نویسنده
چکیده
cu lty R es ea rc h N ew sl et te r 4 that lie on the circle and take only the ones inside it. Given points P and Q in our space, the "line through P and Q" is interpreted as the arc of the circle through P and Q that intersects C at right angles (see Figure 1). With these interpretations of the words "point" and "line", it can be shown that the fifth postulate fails because given a line L and point p outside L, there will be more than one line passing through p that does not intersect L, while Euclid’s other axioms all remain valid.
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