Backing: Why a Rectangle is bigger than a Square
07-19-2012, 06:07 PM
#1
Super Member
Thread Starter
Join Date: Jun 2009
Location: Tavistock, Ontario, Canada
Posts: 1,056
Backing: Why a Rectangle is bigger than a Square
07-20-2012, 03:40 AM
#6
Power Poster
Join Date: Mar 2011
Location: western NY formerly MN, FL, NC, SC
Posts: 51,433
Originally Posted by Rubesgirl
I'm math challenged on my good days! This seems totally improbable. If you take the square and reposition the parts without adding on, it should be the same no matter what... right?
07-20-2012, 02:02 PM
#9
Super Member
Join Date: Jun 2010
Location: Vermont
Posts: 6,977
the solution, courtesy of Google (of course)
actually these fit in the category of optical illusions
In the first diagram, the red and blue triangle have different angles. W/o using trig, you can see the slope of the red triangle is portrayed as 2/5, while the blue triangle is portrayed as 3/8. In the picture with emboldened lines, the eye can't see the difference between .4 and .375, but it is there. If the angles were the same, the blue triangle would intersect halfway between the first 2 graph points, and in the second portion of that diagram, the blue shouldn't actually cover the 8 spaces spanned by the green and light blue figures. The hole comes from the fact that you cannot calculate the total area of the first triangle as (13*5)/2=32.5, because in actuality, keeping the angles to be the same, it's (12.5*5)/2=31.25. In the second picture, to keep the angles the same, you would have to add the areas because the blue wouldn't complete a triangle, so blue=7.5*3/2=11.25, green=8,lblue=7,red=2*5/2=5, total is magically 31.25
The second diagram is the same principal, the angles that are being matched between the 2 symetrical orange pieces and the 2 symetrical green pieces don't match. Again, .375 vs .4, the unseen gap is what equates to the differing apparent areas.
actually these fit in the category of optical illusions
In the first diagram, the red and blue triangle have different angles. W/o using trig, you can see the slope of the red triangle is portrayed as 2/5, while the blue triangle is portrayed as 3/8. In the picture with emboldened lines, the eye can't see the difference between .4 and .375, but it is there. If the angles were the same, the blue triangle would intersect halfway between the first 2 graph points, and in the second portion of that diagram, the blue shouldn't actually cover the 8 spaces spanned by the green and light blue figures. The hole comes from the fact that you cannot calculate the total area of the first triangle as (13*5)/2=32.5, because in actuality, keeping the angles to be the same, it's (12.5*5)/2=31.25. In the second picture, to keep the angles the same, you would have to add the areas because the blue wouldn't complete a triangle, so blue=7.5*3/2=11.25, green=8,lblue=7,red=2*5/2=5, total is magically 31.25
The second diagram is the same principal, the angles that are being matched between the 2 symetrical orange pieces and the 2 symetrical green pieces don't match. Again, .375 vs .4, the unseen gap is what equates to the differing apparent areas.
07-20-2012, 04:09 PM
#10
Super Member
Join Date: Jan 2011
Location: Knot Merrill, Southern Indiana
Posts: 5,781
PTQuilts - thanks for the "translation"
I actually see it now ... look close at the red triangle and the green triangle - especially when matched to each other in the rectangle - and you will see that where the two meet to make a completed square of both red and green ... it's not a true square.
I actually see it now ... look close at the red triangle and the green triangle - especially when matched to each other in the rectangle - and you will see that where the two meet to make a completed square of both red and green ... it's not a true square.
Thread
Thread Starter
Forum
Replies
Last Post
judylg
Main
65
06-14-2012 07:07 PM
DawnMarie
Pictures
2
11-23-2011 03:51 PM
