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這怎麼可能是真的?
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Rosy
雷尚淳
yinghsuan
Jenny say阿彌陀佛!
恰恰
極墨
歐陽玉敏

‧新月‧
就是瑜(小魚)

這個「空格」從那兒來的? 

上面四個不同顏色的圖形,可以任意調動…

聰明的你…快告訴我…﹗

第二張圖案,四個不同顏色圖形面積,與第一張圖案的圖形完全一樣!

但是…如果二張圖案的面積完全一樣…

那麼,第二張圖案的這個「空格」是從那兒來的呢?



本文於 修改第 3 次
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引用網址:http://city.udn.com/forum/trackback.jsp?no=55869&aid=4254620
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Answer is here!
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Rosy
雷尚淳
‧新月‧
就是瑜(小魚)
極墨

How Can This Be True - Answer

1. For both of the pictures to be exactly the same, they must both
have the same area AND each of the pictures must have same area as the
area of the "PERFECT" triangle (
oh no - shades of dreaded Math come to mind!) ...
Here are the calculated areas 4U:

Hint: 
the area of a triangle = 1/2bh
where b is the base and h is the height

1A. Before looking at either picture, calculate what the area of this picture
would be if it was a PERFECT triangle (i.e. 13 X 5 squares)
Area = 1/2bh = 1/2(13)(5) = 65/2 = 32 1/2

1B. Area of the top picture
Area = 1 + 2 + 3 + 4

= 1/2(5)(2) + 1/2(8)(3) + 7 + 8
= 5 + 12 + 7 + 8 = 32

1C. Area of the lower picture
Area = 1 + 2 + 3 + 4 + 5

= 1/2(5)(2) + 1/2(8)(3) + 7 + 8 + 1
= 5 + 12 + 7 + 8 + 1 = 33

Neither of the two pictures form a perfect triangle,
but both of them look very close to the outline of a perfect triangle!

 




2. Compare the slopes of the triangles and you realize that
the hypotenuse of the overall triangle is not a straight line ...

Hint: 
the slope of a line = rise / run
(the slope of a horizontal line is zero)

2A. Slope of the PERFECT triangle
Slope = rise / run = 5 / 13 = 0.384615

2B. Slope of Triangle 1 (in both pictures)
Slope = rise / run = 2 / 5 = 0.4

2C. Slope of Triangle 2 (in both pictures)
Slope = rise / run = 3 / 8 = 0.375

Prove it by blowing up the images and running a ruler along the
hypotenuse of both triangles - both are not a perfect line (but close!)



 




3. The bottom triangle has ~181.2 degrees when by definition a triangle must have only 180 degrees. I used the inverse tangent function and applied it to both angles that were not right angles. I calculated both what the angles should be based on the lengths of the whole triangle at the bottom and what they actually were based on the smaller triangles that formed the angles. The top right angle of the bottom triangle should be ~68.96 degrees based on tan^-1(13/5) but when you input the lengths of the smaller angle into this formula (tan^-1(8/3)) the angle comes out to be 69.44 degrees. Likewise with the other angle it should be ~21.04 degrees and actually is ~21.8. Larger angles mean more area into the shape.


 



Conclusion:  the 2 objects are NOT triangles
(even though they at first appear so!)
and they have different areas...

 

 

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引用網址:http://city.udn.com/forum/trackback.jsp?no=55869&aid=4256099