Axiom talk:Euclid's Axiom
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If I read correctly, the source states an angle $bac$, and furthermore Figure 9 appears to apply. --Lord_Farin 14:47, 24 January 2012 (EST)
- ...don't know how I missed that. --GFauxPas 14:50, 24 January 2012 (EST)
- $m\angle bac \le 180^\circ$ depends on if you insist that $\angle bac = \angle cab$ (if you don't, you have to specify a standard direction (clockwise or anticlockwise) for measurement; a pain in practice, and probably undesirable as well). P.m., could you remind me which of the following is UK English: anticlockwise, counterclockwise. Thanks. --Lord_Farin 17:14, 24 January 2012 (EST)
- Anticlockwise is UK, counterclockwise is US. I found this out when people didn't know what I was talking about when I was briefly in England. Every book / video / class I've seen has always had the origin as the positive x-axis and the angle measured counterclockwise. Though that doesn't mean much, as I haven't seen that much. In any event, Tarski's list of undefined terms doesn't include "angle" or "line", so I'm not sure what to do. --GFauxPas 17:21, 24 January 2012 (EST)
- Thanks for clarifying. I would say that such a definition works just fine in two dimensions, but higher-dimensional analogues are bound to be cumbersome. I retract the $\angle bac = \angle cab$ assumption when I recalled high school upon your comments (where it was insisted that the points constituting an angle would be in specific order). It appears as though the angle example fails rather than that the axiom is inconsistent, i.e., the transition from axiom to intuition isn't flawless. But I'm not sure. --Lord_Farin 17:50, 24 January 2012 (EST)
- That was my inclination, that it's just a snag in the transition to intuition. The real axiom is a statement about the placement of dots. Though I can illustrate this axiom to myself by drawing dots on paper, it would be rather difficult to explain it in a static diagram. --GFauxPas 17:55, 24 January 2012 (EST)
- Thanks for clarifying. I would say that such a definition works just fine in two dimensions, but higher-dimensional analogues are bound to be cumbersome. I retract the $\angle bac = \angle cab$ assumption when I recalled high school upon your comments (where it was insisted that the points constituting an angle would be in specific order). It appears as though the angle example fails rather than that the axiom is inconsistent, i.e., the transition from axiom to intuition isn't flawless. But I'm not sure. --Lord_Farin 17:50, 24 January 2012 (EST)
- Anticlockwise is UK, counterclockwise is US. I found this out when people didn't know what I was talking about when I was briefly in England. Every book / video / class I've seen has always had the origin as the positive x-axis and the angle measured counterclockwise. Though that doesn't mean much, as I haven't seen that much. In any event, Tarski's list of undefined terms doesn't include "angle" or "line", so I'm not sure what to do. --GFauxPas 17:21, 24 January 2012 (EST)
- $m\angle bac \le 180^\circ$ depends on if you insist that $\angle bac = \angle cab$ (if you don't, you have to specify a standard direction (clockwise or anticlockwise) for measurement; a pain in practice, and probably undesirable as well). P.m., could you remind me which of the following is UK English: anticlockwise, counterclockwise. Thanks. --Lord_Farin 17:14, 24 January 2012 (EST)