1.
在矩形ABCD中,若\( \overline{AB}=2 \)、\( \overline{BC}=2 \sqrt{3} \),過\( \overline{AC} \)的中點O作\( \overline{EF} \perp \overline{AC} \)交\( \overline{AD} \)於E、交\( \overline{BC} \)於F,將平面ABFE沿\( \overline{EF} \)摺起,使得平面ABFE垂直平面CDEF,求此時\( cos∠BFC= \)?
設有一張長方形的紙ABCD,已知\( \overline{AB}=8 \),\( \overline{BC}=4 \),通過對角線\( \overline{BD} \)的中點M且垂直於\( \overline{BD} \)的直線分別交\( \overline{AB} \)與\( \overline{CD} \)於E、F兩點,當以\( \overline{EF} \)為折線把紙ABCD折起來,使得平面AEFD垂直於平面EBCF,此時若\( ∠CFD=\theta \),\( 0<\theta<\pi \),則\( cos \theta= \)?
(100學年度北區第二次模擬考數甲,
http://web.tcfsh.tc.edu.tw/jflai/rab/RA660.swf)
解答
https://math.pro/db/viewthread.php?tid=567&page=1#pid5066
5.
由邊長為1的正三角形堆疊n層,試問邊長為6時(即\( a_6 \) ),所有大大小小之平行四邊形總數為
102.3.28補充
有多少個平行四邊形?
http://books.google.com.tw/books ... e&q&f=false
102.4.23補充
The sides of an equilateral triangle ABC are divided into n equal parts ( \( n \ge 2 \) ). For each point on a side, we draw the lines parallel to other sides of the triangle ABC, e.g. for \( n=3 \) we have the following diagram:

For each \( n \ge 2 \) find the number of existing parallelograms.
(Canada National Olympiad 1991,
https://cms.math.ca/wp-content/uploads/2019/07/exam1991.pdf)
110.5.3補充
設\(\overline{AB}\)為圓\(x^2+y^2=37\)的一弦,若點\(P(1,2)\)在\(\overline{AB}\)上,且為\(\overline{AB}\)的三等分點之一,試求直線\(AB\)的方程式
。
(110彰化女中,
https://math.pro/db/viewthread.php?tid=3514&page=1#pid22759)