Looks ok to me..
The old where did the square go routine
Three is two is one is everything
Let a,b be any pair of numbers. Without loss of generality,say a = b + c, for some number c.
=> a^2 - ab = ab + ac - b^2 - bc
=> a^2 - ab - bc = ab - b^2 - bc
=> a(a - b - c) = b(a - b - c)
=> a = b, for arbritrary a,b.
Why its wrong:
a=b-c, so a-b-c=0,and we all know how bad dividing by zero is..
A five colour problem in 2D
The old "I know what number you're thinking" routine
With links to similar feats of magic.
Pythagorus is wrong!
As I posted to the Unisfa mailing list some time ago:
Could someone please show me where I'm wrong?
When I was in primary school I used to have to climb this large hill to
get home. One day in year 6 or 7 I was crossing the road from side to
side,to kill the boredom,and I thought to myself -"If I'm going from
here to a point forward and accross the road,is it quicker to cross
diagonally,or to go straight across,and then walk up?"
Pacing was inconclusive (They seemed about the same) so I did a bit of
simple mental calculus (Of a sort)..(Not as mathsy as this,of course)
Call the road width x,and the forward distance to the house y (Ie a right
angled triangle of width x and height y)
Approximate the hypotenuse by a zigzag.All the accross bits add up to x,and all the up bits add up to y,giving a
total length of x+y.
So,if you take the limit as the number of divisions tend to infinity (Ie
all the little ziz-zag bits getr smaller and smaller),shouldn't you still
get x+y?
I later saw a proof of pythagoruses theorem in a book,but decided it
lacked elegance (Maybe why this is why I still have problems with trig..)
Why this isn't true:
Measure it. It isn't. Also the proof needs the step "..hence dx+dy tends to dh for small enough dh" (h being the hypotenuse,duh) or it's meaningless.
Scott Adams' Crackpot Theory
As in Dogbert Newsletter 26. I know this is sheer copying,but its a cool theory
----
Imagine an object moving between two points. The normal view is
that the object occupies each and every position on its path until
it reaches its destination. But the number of possible positions
between any two points is infinite. Does it make sense that an
object could occupy infinite positions in space in a finite period
of time?
Let's say no, or else my crackpot theory falls apart.
Under my crackpot theory, objects actually disappear and then
reappear along their path. They only seem to move because it
happens so quickly. Slow objects pop into existence slightly ahead
of their last position. Fast objects pop into existence far ahead
of where they were last; that's what makes them seem fast. So for
any given distance, the fast-moving objects pop into existence
fewer times along the path, like a long-legged runner who needs
fewer strides.
A fast-traveling clock, for example, would have less time in
existence to tick. If you could see it whizzing past you, it would
appear slow.
Obviously all of this popping in and out of existence would have to
be happening so fast we can't notice or measure it.
It might seem impossible that objects pop in and out of existence.
But physicists know that's exactly what happens in the super-tiny
quantum world. Matter jumps in and out of existence continually.
Although large objects don't play by the same rules as the quantum
world, the squirrelliness of the tiny world makes you question what
you really know about anything.
---
Hey,who says this is wrong?(Thats right,I can't be bothered refuting it)Though I will say that the number of positions between two points is finite,effectively, due to the whole uncertainty principle/Planks constant thing.
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