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Equable shape
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Equable shape : ウィキペディア英語版
Equable shape
A two-dimensional equable shape (or perfect shape) is one whose area is numerically equal to its perimeter. For example, a right angled triangle with sides 5, 12 and 13 has area and perimeter both have a unitless numerical value of 30.
==Scaling and units==
An area cannot be equal to a length except relative to a particular unit of measurement. For example, if shape has an area of 5 square yards and a perimeter of 5 yards, then it has an area of and a perimeter of 15 feet (since 3 feet = 1 yard and hence 9 square feet = 1 square yard). Moreover, contrary to what the name implies, changing the size while leaving the shape intact changes an "equable shape" into a non-equable shape. However its common use as GCSE coursework has led to its being an accepted concept. For any shape, there is a similar equable shape: if a shape ''S'' has perimeter ''p'' and area ''A'', then scaling ''S'' by a factor of ''p/A'' leads to an equable shape. Alternatively, one may find equable shapes by setting up and solving an equation in which the area equals the perimeter. In the case of the square, for instance, this equation is
:\displaystyle x^2 = 4x.
Solving this yields that ''x'' = 4, so a 4 × 4 square is equable.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Equable shape」の詳細全文を読む



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