Educated Earth // Videos - Mathematics - Missing Square
User:
Pass:
Remember Me
Forgot Pass Register

Our educational work is entirely supported by people like you. Your donations directly add new exhibits and new features to the website, and even helps us open the Prehistoria Natural History Center!




eXTReMe Tracker

Videos / Mathematics / Missing Square







Missing Square

Missing Square
Rearrange pieces of a triangle and a square goes missing. Is it magic or math?


  • Currently 2.88/5
  • 1
  • 2
  • 3
  • 4
  • 5
Rating: 2.9 / 5 (989 votes)
Posted by nova on August 9, 2007
Hits: 5325

More Videos

Dawn: Mission to the Astroid Belt
Dawn: Mission to the Astroid Belt
Type: Astronomy
Black Hole Destroys A Neighbouring Star
Black Hole Destroys A Neighbouring Star
Type: Astronomy
Electrolytes
Electrolytes
Type: Physics & Chemistry
The Hobbit Of Flores
The Hobbit Of Flores
Type: Humanity
Life of a Star
Life of a Star
Type: Astronomy
Jupiter Icy Moon Orbiter
Jupiter Icy Moon Orbiter
Type: Astronomy
Leopard vs Hyena vs Lion
Leopard vs Hyena vs Lion
Type: Life on Earth
Black Hole Montage
Black Hole Montage
Type: Astronomy
Fluorescence of Various Materials
Fluorescence of Various Materials
Type: Physics & Chemistry
Robonaut 2 Joins The ISS Crew
Robonaut 2 Joins The ISS Crew
Type: Astronomy
Robot Adapts To Various Terrains
Robot Adapts To Various Terrains
Type: Tech & Gadgets
Constellation Mission Animation
Constellation Mission Animation
Type: Astronomy
Amory Lovins - 50 Year Energy Plan
Amory Lovins - 50 Year Energy Plan
Type: Tech & Gadgets
Cannonball Dropped Into Mercury
Cannonball Dropped Into Mercury
Type: Physics & Chemistry
Goats Playing On Flexible Steel
Goats Playing On Flexible Steel
Type: Life On Earth

Comments

Posted by John Q. Public on August 9, 2007 at 11:08 am
This is an old puzzle. The "trick" is that the outer figure does not form a real triangle.

Look at the two smaller triangles. The sides of the larger triangle are 3 x 8. The sides of the smaller triangle are 2 x 5. So the triangles are not actually similar. (That is to say, the blue is not really a reduced version of the red... their angles are different.) The long side of the outer figure, then, is not really a straight line. It bends ever so slightly where the two triangles touch. This is also true of the bottom figure when rearranged.

So while the outer figures look like two triangles at first glance, they are actually 4-sided because of the slight bend.

Because the two smaller triangles do not have the same internal angles, when rearranged the other pieces fit together differently. This creates the illusion of gaining a space.
Posted by kimmy on August 9, 2007 at 8:31 pm
This is like the old joke about 3 people renting a room.
The clerk said $30 for the night.
Each paid $10 for the room.
Later that evening the Manager said that the clerk overcharged the persons.
It should have been $25 for the night.
The clerk was given $5 to return to the 3 guys.
He figured that 3 into 5 wouldn't go.
So he gave each person 1$ in refund.
Each person gave $10 for the night.
Each person got back $1.
Do the math!
Each person gave $10.
Each person got back $1.
The clerk kept $2.
3x9=27.
The $2 the clerk kept= 29.
Whatever happened to the other dollar?
Posted by John Q. Public on August 13, 2007 at 9:59 am
I could answer but probably shouldn't.

I should also have placed a "spoiler warning" on my first post.
Posted by John Q. Public on August 13, 2007 at 10:02 am
Hmmmm... well, here is a hint for readers, without actually giving it away. The trick is to pay attention to where the money ends up, not who paid how much.
Posted by Jangaly_x on September 5, 2007 at 6:45 am
In the second arrangement the hypotenuse is not in the straight line. This results the second arrangement takes more area, to compensate must a squqre must be left.
User: Pass: Remember Me

To comment on this item, please login or register.


Warning: Unknown: Your script possibly relies on a session side-effect which existed until PHP 4.2.3. Please be advised that the session extension does not consider global variables as a source of data, unless register_globals is enabled. You can disable this functionality and this warning by setting session.bug_compat_42 or session.bug_compat_warn to off, respectively in Unknown on line 0