It's time to be a nerd again everyone! :D
Mathematical illusion number 1:
let say a=b
then let’s multiply the equation by a so that this will become
a²=ab
after multiplying, add -b² to the equation so that it will become
a²-b²=ab-b²
then factor out the equation.
(a+b)(a-b)=b(a-b)
divide the whole equation by (a-b)
a+b=b
back to the top we know that a is equal to b so we can change the a to b or the b to a.
let’s say the a to b
a+a=a and
2a=a
then divide the whole equation by a so that
2=1 ???
Mathematical illusion number 2:
if you can't see the whole image, click here > Illusion number 2
Just view the animation and don't mind the chinese characters in it. They just mean "A", "B", "C" and "D" like in geometry.
Mathematical illusion number 3:
Three friends check into a motel for the night and the clerk tells them the bill is $30, payable in advance. So, they each pay the clerk $10 and go to their room.
A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return $5 to the 3 friends who had just checked in.
The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day!
Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 which was originally spent.
Where did the other dollar go????
Bonus illusion! (with answer to be posted soon, unless someone posts it in the comment section)
We all know that the roman numeral for 10 is X and Nine is IX. Draw a single continuous line and turn IX into 6. The only stipulation is that the pen could not be lifted from the paper until the line was complete.
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Wednesday, October 29, 2008
3 mind boggling mathematical illusions
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9 comments:
if an "S" is a continuous line, then SIX
a-b=0 and you cant divide by zero
**SPOILERS**
1. If a=b then a-b=0, so to get from line 4 to 5 you would have to divide by zero.
2. The line in the centre isn't straight because sides of the two different parts have gradient 3/8 and 2/5
3. The room cost $25 not $27, since the refund was $5. The friends paid $9 each = $27 = $25 for the room and $2 for the bellhop.
The first "illusion" is clearly invalid because it divides by zero, which isn't meaningful.
Given: a=b
a²=ab
a²- b²=ab-b²
Note that a²- b² = a²- a² = 0
(a+b)(a-b)=b(a-b)
Note that (a-b) = (a-a) = 0
a+b=b
Can't do this because you are dividing by 0. That's why this doesn't work.
In "Mathematical illusion number 1"
a=b implies a-b = 0
When you divide both sides of the equation by a-b, you are dividing both sides by 0 therefore you are making an invalid operation.
Your "proof" fails at that point.
I didn't want to spoil the fun that's why I didn't put answers :)
ayokong magcomment kasi hindi ako nag BS Math. lol
in the third one, the clerk takes out five dollars from 30 which leaves 25. Dollars number 26, 27, and 28 are returned to the guests and the bellhop pocketed dollars 29 and 30
the answer to the last one is so simple....just draw a letter S without lifting a pen to make it six...
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