不懂如何入手,望高人指教.
更新1:
一樓答案對了, 但我用微積分方法解決, 期盼回答~
微分的應用問題
2008-10-20 8:59 pm
A lattice point in the plane is a point with integer coordinates. Suppose that circles with radius r are drawn using all lattice as centers. Find the smallest value of r that any line with slope 2/5 intersects some of these circles.
不懂如何入手,望高人指教.
不懂如何入手,望高人指教.
回答 (1)
2008-10-21 1:47 am
✔ 最佳答案
這似乎由三角幾何來做較快.由 y=(2/5)x 開始往上移, x^2+y^2=r^2 或 (x-2)^2+(y-1)^2=r^2 會最接近 y=(2/5)x+c.
y=(2/5)x+c 接近 x^2+y^2=r^2 時,
c=sqrt(29)r/5
y=(2/5)x+c 接近 (x-2)^2+(y-1)^2=r^2 時,
c=1/5-sqrt(29)r/5
因兩個 r 是相同, 故 c=sqrt(29)r/5=1/5-sqrt(29)r/5=1/10
r=1/[2*sqrt(29)]=0.093
因太久沒有玩數學, 如有錯誤, 祈為指正.
參考: my knowledge
收錄日期: 2021-04-23 12:54:43
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081020000051KK00602