A Fallacy in Mathematics is an apparently correct logical argument which leads to an incorrect conclusion.
Now let a=1, and hence 1+1=1.
- $a+a=a$ (as a=b)
- Hence $-1=1$
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.
Therefore all obtuse angles are right angles.
- 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
Similarly all acute angles are right angles (complement of obtuse angles) ... all angles are right angles.
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