點先可以只係用一個圓規,畫一個等邊等角既5邊形呢??
回答 (3)
2006-11-20 2:21 am
✔ 最佳答案
Maybe you can't ................圓規can;t do it
2006-11-20 7:48 am
Thx for your question. This gives me a initiative to find the sol'n.
To construct a right angle triangle with adjasent sides of lenght 1 and 2, we will then obtain sqrt(5) and hence { sqrt(5) - 1 }.
Now, construct a right angle triangle with adjasent sides of lenght { sqrt(5) - 1 } and 2, we will then obtain sqrt{ 10 - 2 x sqrt(5) } . Let this number be 2L.
Finally, construt a circle with radius one and then use L to intersect the circumference of the circle, we will obtain the required pentagon!!
2006-12-02 17:05:49 補充：
Yes. Just use compass ( 圓規 ) can't do it. It could only be done by ruler and compass together.
To construct a right angle triangle with adjasent sides of lenght 1 and 2, we will then obtain sqrt(5) and hence { sqrt(5) - 1 }.
Now, construct a right angle triangle with adjasent sides of lenght { sqrt(5) - 1 } and 2, we will then obtain sqrt{ 10 - 2 x sqrt(5) } . Let this number be 2L.
Finally, construt a circle with radius one and then use L to intersect the circumference of the circle, we will obtain the required pentagon!!
2006-12-02 17:05:49 補充：
Yes. Just use compass ( 圓規 ) can't do it. It could only be done by ruler and compass together.
2006-11-20 2:29 am
先畫一條直線,將圓規調較與直線長度一樣的闊度,在直線的左邊畫出一個弧度,再在直線的右邊畫出另一個弧度,就會得出一個相交點,再把五點連起來,這就是等邊五角形
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