Another brain fuzzer.

 

Alan, you have WAY too much free time.

 

What in the...

I can't look at that anymore
lol

 

The slope of the red and green triangles are not the same therefore what appears to the eye to be large right angle triangle is not. By placing the red triangle (s= .375) on the bottom the longest line is slightly concave whereas with the green triangle s= .400 on the bottom the line is now slightly convex I didn.t do the math but im pretty sure the difference in area would add up to 1 unit.(hole). Now I got a headache.

Alan stop screwing with peoples heads.

Skip_T

1934 Ford PU

 

Is your monitor playing tricks on you? Try printing it out.

 

I figured it out, its the way the peices are aranged. I printed it out cut out the bottom one and laid it over the top one in the same order as the top one and it matches.

 

Alan

Of coarse my monitor is playing tricks on me, if it couldn't fool my sense of perception it wouldn't work. However the math of what you show can't.

Slope (rise in units per unit) = height (in units)/ base (in units)

Red Triangle 3 / 8 = .375 per unit
Green Triangle 2 / 5 = .400 per unit

Therefor the long line in the drawings can't possibly be a stright line but slightly arched and the direction of the arch depends on the placement of the triangles. In the upper fiqure, the arch is downward toward the base In the lower figure it is arched upward away from the base giving the lower figure more area as the pattern areas are fixed this area must show up somewhere hence the hole. A clever play on preception but the math dont lie.

Skip_T

 

Skip's right, the green has a rise of two in a run of five. At an equal slope, the red would have to have a rise of 3.2 in a run of eight instead of the 3 you see in the picture.
run - 5 x 1.6 = 8
rise - 2 x 1.6 = 3.2

 

I printed this out, & all of the pieces appear equal, however, I agree that the two triangles have different slopes(mathematically, although I can't see it). If you use the equation for the area of a triangle (LxHx1/2), which would be 13x5x1/2, you get 32.5. However, if you do this for each individual triangle,(5x2x1/2 & 8x3x1/2) you get 5 & 12 + 15 for the other two shapes, which equals 32. Even that difference of 1/2(area) wouldn't explain the entire square of extra space. I can't understand this & it makes my head hurt. I might even lose sleep over this. Maybe I need to go back to high school & take geometry again.

 

I drew this out on AutoCAD, and it is true, the apparent hypotenuses of the overall triangles are not a straight line, but rather two lines with slightly different angles. If a true hypotenuse is drawn, a gap of .071796 can be seen between the true hypotenuse and the point where the green and red triangles meet.

The length of the red hypotenuse= 8.544004
The length of the green hypotenuse= 5.385165
The length of the true overall hypotenuse= 13.928388

If you fom a triangle with these three figures, the area comes to exactily .500000.

 

And you can see it on the monitor. On the bottom "triangle", from the left corner, go 5 units to the right and 2 up. You will see that it meets at a grid intersection. The top "triangle" shows it's "hypotenuse" is slightly below the similar grid intersection.

 

I guess when you arrange certain shapes, little spaces like that are unavoidable.

For example, I printed out the word 'hypotenuse' 7 times, and then cut it out and stacked all seven pieces on top of each other. After I was done, there was a tremendous space savings.

Just kidding around.

Jared

 

having nothing better to do, I fired up the network printer, and printed the thing out. Three times. just to make sure. Then I carefully cut out each of the sections, twice, just to be sure. I then checked each one to see if they were all the same corresponding size, which they were. All lines were perfectly straight - used a straight edge, and all the same as the corresponding section. This proved that there was no trickery going on, and managed to prove, utterly conclusively, that it is very easy to totally confuse me.

However, my much younger and brainier Math Major Engineer wife decided that she would look at it too. She does not have the fog of advancing years to cloud her mind and judgment, so she will look at it very logically, and think for an hour or two, (whilst I go hide the REMOTE) and then she too will admit, that she is also very easy to confuse.

Either that, or she will prove the superiority of the sexes, and show us all up. (which I doubt, being male, and Australian.)

Alan, I would like to know the answer to this one, so if you don't know it, HIDE.

This is the only post anywhere, to get my wife sat on the floor, with scissors straight edges and razors, playing with printouts, at 00:15.. She was about to go to bed, but I think I will be asleep LONG before she is tonight...


This is a very good conundrum!!

Theo

 

Theo, if she can figure this one out, I will bow down to every female I see for the next week.

 

At the risk of being laughed at, I'll take a stab at it.............

By swapping the red and the dark green triangles, you wind up lengthening the run and shortening the rise of the bottom right rectangular portion of the comprised triangle (the tan and light green portion). The reason the length of the entire comprised triangle doesn't change is because the run of the green triangle is shorter, and the rise of the red triangle is taller.

Am I close, or is this the part you guys already know?