Hi everyone . I have been bogged down by this question for ages . I confirm through 2 different methods what the answer is, and the course book (isbn 0435516043 - section Mics. 5.10 question 11) gives a diffenet answer. It is either a typing error or I am screwing up somewhere. Can someone please try this out to help me confirm. Here is the question.
You have a pentagram. At its centre is a naturally occuring pentagon (five pointed). then of course the five equilateral triangles around that, making up the pentagram. the longest side of these equilateral triangles is x. Also there is a bisect in the pentagon. check out the image:
well, it looks like i can not upload a picture from my computer. So I will have to describe it instead.
Take a circle. A pentagon fits inside the circle, with its edges just kinssing the circumference. therefore, each side of the pentagon has a curve slightly above it, i.e. the perimeter of the circle. The length of these arcs is 1 unit. Therefore I calculated the circumference to be 5 units. The sides of the pentagon have equilateral triangles on them, such that, the pentagon and the triangles form a pentagram. the two equal sides of each equilateral triangle is marked x. Also, it happens that if you take a chord line in the pentagon to form another equilateral triangle, its base side (the side of the triangle that is not one of the two equal sides) is also equal to x. Now if you draw this out, hopefully you will be seeing roughly what I am seeing. This is all the information I was given along with the following question:
The shape below is known as a pentagram. Find x.
I calculated x to be 1.52 (2 d.p.). this answer came about from using two mathematical methods. Now, the book, however gave the answer to be 1.1618. What the hell, I thought .
Please, could someone, or as many as possible go through this question to find out who is wrong here, the book editor or me (most likely me). If any of you do find me to be wrong, please take me through how you work the answer out, to be as what the book says?