One way to construct a regular pentagon Take five ball-point pens or other objec

Question

One way to construct a regular pentagon Take five ball-point pens or other objects of equal length(call it 1) and arrange them symmetrically, as shown in the diagram above, so that O, A, C and O, B, D are collinear and |OC| = |OD|. Let AO = v, |BO| = |v|, CD = w, CA = xv, |DB| = x|v|. Express vectors AD and OB in terms of x, v, and w. By using the fact that these vectors have the same length 1 as v and w, get two equations relating x and v middot w. (Use the distributive law for the dot product). Eliminate x to find a quadratic equation satisfied by v middot w. Show that the angle alpha between v and w satisfies the equation sin 3 alpha = - sin 2alpha and that therefore alpha = 2 pi/5.(In case you have forgotten, sin 3 alpha = sin alpha (4 cos^2 alpha - 1)).

Explanation / Answer

Please note that the given problem is related to advanced Mathematics. Kindly post the question in appropriate medium. Thank you, and wish you all the best.

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.