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April 15th, 2014, 03:40 AM   #1
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How many petals do the T8 and T9 flowers have? I can't count it . :/

For the number sequence that you have generated, find the values of and . Express each answer as a decimal.
Based on your answers, form a conjecture. Prove it.
(c) Determine the value of correct to four significant figures.
Your answer for part (c) above is known as the golden ratio. The Greeks observed that this is a pleasing dimension for a building or any structure. Thus, if a rectangle of length y cm and width x cm, where y > x, is such that , then it is a golden rectangle with a pleasing dimension.

(d) Identify 5 different types of products with rectangular surfaces. For each type of product, collect a few items with different sizes. Based on the products that you have collected, determine whether product marketing nowadays exhibits the golden ratio.

(e) (i) You are given the following information:

Determine whether such rectangles are golden rectangles.
(ii) You are now given a general case:

Determine whether such rectangles are golden rectangles.
(iii) The width of a golden rectangle is 8 cm.
Find its length. Use two methods.
(iv) You are given two pieces of wire, each 20 cm long. One piece is to be bent to form the biggest possible rectangle and the other piece to form a golden rectangle. Determine the length and width of each rectangle.
Use two methods in each case.
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April 16th, 2014, 07:55 AM   #2
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Quote:
 Originally Posted by jiasyuen For the number sequence that you have generated, find the values of and .
Of what and what? There appears to be information missing here and at other places in your post.

What are T8 and T9 flowers?

April 16th, 2014, 08:02 AM   #3
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[QUOTE=greg1313;190939]Of what and what? There appears to be information missing here and at other places in your post.

Sorry.

This is the question.
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Last edited by jiasyuen; April 16th, 2014 at 08:50 AM.

 April 16th, 2014, 08:47 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2201 The petal counts for T1 to T9 are 1, 1, 2, 3, 5, 8, 13, 21 and 34, which are successive terms of the Fibonacci sequence. The ratio of successive terms approaches (1 + sqrt(5))/2 = 1.618 (to 4 significant figures). Adding any two successive terms in the sequence gives the next term in the sequence. In (d), the word "products" means physical things that are produced, rather than having its mathematical meaning. For e(1v), the rectangle that is biggest (in area) is a 5cm by 5cm square. The required golden rectangle is (20 - 10t) cm wide by (10t - 10) cm long, where t is the golden ratio. For the questions that I haven't answered, please clarify where appropriate and post your attempts if you still need help. Last edited by skipjack; April 16th, 2014 at 08:52 AM.
April 16th, 2014, 08:52 AM   #5
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Quote:
 Originally Posted by skipjack The petal counts for T1 to T9 are 1, 1, 2, 3, 5, 8, 13, 21 and 34, which are successive terms of the Fibonacci sequence. The ratio of successive terms approaches (1 + sqrt(5))/2 = 1.618 (to 4 sigmificant figures). Adding any two successive terms in the sequence gives the next term in the sequence. In (d), the word "products" means physical things that are produced, rather than having its mathematical meaning. For e(1v), the rectangle that is biggest (in area) is a 5cm by 5cm square. The required golden rectangle is (20 - 10t) cm wide by (10t - 10) cm long, where t is the golden ratio. For the questions that I haven't answered, please clarify where appropriate and post your attempts if you still need help.
I've posted the missing photo. Please see it. Thanks!

 April 16th, 2014, 08:59 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2201 The extra part of the image doesn't have sufficient resolution. From what I can see, the questions are easy enough for you to attempt, especially if you used the link I provided first.
April 16th, 2014, 09:05 AM   #7
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Quote:
 Originally Posted by skipjack The extra part of the image doesn't have sufficient resolution. From what I can see, the questions are easy enough for you to attempt, especially if you used the link I provided first.

I can't really find the answer. Can you give me some guides for them?
By the way, what is conjecture? How to prove it?
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 May 22nd, 2014, 08:53 AM #8 Newbie   Joined: May 2014 From: JB Posts: 2 Thanks: 0 add math project work 2014 Assignment No. 4 Assignment No. 3.i need help to complete my work

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5 different types of products with rectangular surfaces exhibits the golden ratio.

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