Section+4.3+The+Sexiest+Rectangle

We are all going to use the wiki to discuss problems assigned. Look below and you will find the problem that you are responsible to post the first answer for based on your Aquinas e-mail address. It is NOT o.k. to just write "I don't get it". Start by typing the problem (click on edit to start) word for word from the book. You Post your answer as if it were a test question ( You would not leave those blank you would take a stab at it!), HOW you got it (list specific page references and show work) and WHY you did that way. The rest of the class will make comments, on at least 3 other problems, corrections, and post their thoughts below your original response.

Mindscapes for Chapter 4.3 please post original response by Friday 10/1(noon) and classmate responses by Sunday 10/3 (noon):

4.3 (1) [JEH003] Will someone please post a response here...anyone! Make sure you put your aq address so that you get credit for posts and comments. mrh003 where are you??? [ShariL] klk002: You can tell if a rectangle is a golden rectangle if the ratio of it's base to it's height equals the golden ratio. and remember the golden ratio ( 1+sqaureroot 5) /2= 1.618 ... There are plenty of examples of golden rectangle in our book, my favorite was Leonardo da Vinci's illustration for Luca Pacioli's De Divina Proportione. And in a golden rectangle, remember that the size is not what is important, it is the ratio of the two sides !

4.3 (2) [nmg002] The golden ratio is (1+ √ 5)/2=1.618…. which rounds up to 1.62. Therefore the closest ratio is 1.62 [trc002]-It took me a while to figure this one cause couldn't find the formula for some odd reason in my book. Looks good! [Shari L]

4.3 (3) [fab001] To find which object is the closest to a golden rectangle we find which is closest to the golden ratio. 5/3= 1.6666 11/8.5= 1.294 14/11= 1.272727 17/11= 1.545454 the 5*3 card is the closest, It is not the golden ration but it is significantly closer than the others.

Nice job. [ShariL]

4.3 (9) [trc002] Yes you would still have a Golden Triangle because golden triangles can be shrunken or expanded. Will someone please post a response here...anyone! Make sure you put your aq address so that you get credit for posts and comments. mrh003 where are you??? [ShariL] klk002 comment: Yes, if you have a Golden Rectangle cut out of paper and if you fold bold the base and the width, you can form a new Golden rectangle. Because, with golden rectangles, you can have all different sizes. If you divide a golden rectangle into a smaller rectangle, the smaller rectangle is also a golden rectangle.

4.3 (12) [mrh003] Take a Golden Rectangle and attach a square so that you create a new larger rectangle. Is this new rectangle a Golden Rectangle? What if we repeat this process with the new larger rectangle? -Golden Rectangles are made up of a smaller golden triangle and a square, so yes the new rectangle is a Golden Rectangle. -Since we started with a Golden Triangle we can repeat this process over and over and keep creating larger and larger Golden Rectangles.

Triangle????[ShariL]

4.3 (17) [SMD001]

4.3 (20) [jtl001]