Most recent change of Fallacy
Edit made on April 20, 2009 by derekcouzens at 06:36:33
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A Fallacy in Mathematics is an apparently correct logical argument which leads to an incorrect conclusion.
!! Fallacy 1: 1+1=1
* EQN:a+a=a (as a=b)
Now let a=1, and hence 1+1=1.
!! Fallacy 2: -1 = 1
* Hence EQN:-1=1
[[[> IMG:angles1.png ]]]
!! Fallacy 3: all angles are right angles
(Rouse Ball's Fallacy)
Construct a quadrilateral ABCD such that AC = BD and angle CAB is a right angle and angle DBA is obtuse.
* AB is therefore not parallel to CD,
** hence perpendicular bisectors are not parallel
** hence perpendicular bisectors intersect at some point: call it E
* Construct the perpendicular bisector of AB namely ME
* Construct the perpendicular bisector of CD namely NE
* Triangle AEM is congruent to triangle BEM (RHS)
** thus angle EAM = angle EBM
* Triangle ACE is congruent to triangle BDE (SSS)
** thus angle EAC = angle EBD
* Subtracting these angles gives angle CAB = angle DBA
Therefore all obtuse angles are right angles.
Similarly all acute angles are right angles (complement of obtuse angles) ... all angles are right angles.