IGVENTURE

rottin' said:
But that pi is messing up the optic....Actually today is Pi Day....3/14 or 3.14🙂
Click to expand...

It's much more than that - it's the once-in-our-lifetime "Rounded Pi Day". Pi to the first five decimal places is 3.14159. If you round that, you get 3.1416, which is today's date. So in honor of this special Rounded Pi Day, here is a problem to solve: prove that the red portion has the same area as the blue portion in the diagram shown here ...

25157607164_592f02aa8c_o.jpg
 
1speed said:
It's much more than that - it's the once-in-our-lifetime "Rounded Pi Day". Pi to the first five decimal places is 3.14159. If you round that, you get 3.1416, which is today's date. So in honor of this special Rounded Pi Day, here is a problem to solve: prove that the red portion has the same area as the blue portion in the diagram shown here ...

25157607164_592f02aa8c_o.jpg
Click to expand...

ok - here is what i'm thinking -

the only thing you need to know is the area of a circle = πr^2 (π times the radius times the radius)

the area of the slice of "pie" is π(r^2)/4 (1/4 of the whole)
the area of the red is the whole slice removing the area of the two inscribed half circles then add the blue back in (cause it was taken out twice) so two half circles make a whole, but the radius is half that of the big slice π(r/2)^2
area of red = π(r^2)/4 - π(r/2)^2 + area of blue

πr^2/4 - π(r/2)^2 = 0 These terms cancel each other out

area of red = area of blue

- ---

on the same note, last year

3/14/15 9:26:53.589.....
 
Last edited:
fidodie said:
ok - here is what i'm thinking -

the only thing you need to know is the area of a circle = πr^2 (π times the radius times the radius)

the are of the slice of "pie" is πr^2/4 (1/4 of the whole)
the area of the red is the whole slice removing the area of the two inscribed half circles then add the blue back in (cause it was taken out twice) so two half circles make a whole, but the radius is half that of the big slice π(r/2)^2

area of red = πr^2/4 - π(r/2)^2 + area of blue

πr^2/4 - π(r/2)^2 = 0

area of red = area of blue

- ---

on the same note, last year

3/14/15 9:26:53.589.....
Click to expand...


Yeah, that's probably quicker than how I did it. I looked at the quarter circle as having area πr^2/4. The two smaller half circles have a radius equal to r/2, which means each of them have an area of 1/2 πr^2/4, or together they have πr^2/4. So the area of the two semi circles is equal to the area of the larger quarter circle. That means that the overlap between them (blue) must be equal to the portion not included (red.) Putting that in equation form collapses to exactly yours, just cosmetically different:

πr^2/4 = (1/2*π(r/2)^2 + 1/2*π(r/2)^2 - blue) + red
or
0 = -blue + red
or
blue = red.
 
1speed said:
Yeah, that's probably quicker than how I did it. I looked at the quarter circle as having area πr^2/4. The two smaller half circles have a radius equal to r/2, which means each of them have an area of 1/2 πr^2/4, or together they have πr^2/4. So the area of the two semi circles is equal to the area of the larger quarter circle. That means that the overlap between them (blue) must be equal to the portion not included (red.) Putting that in equation form collapses to exactly yours, just cosmetically different:

πr^2/4 = (1/2*π(r/2)^2 + 1/2*π(r/2)^2 - blue) + red
or
0 = -blue + red
or
blue = red.
Click to expand...
Justin-Timberlake-Blank-Stare.gif
 
I did a road trip to University of Pitt the last couple of days. Pittsburgh is a beautiful city and the school feeds off this energy with its own section of the city which it shares with Carnegie Melon college. The weather was perfect for the tour, my son Jamie got into Pitt and we did the accepted students day on Tuesday and got some sight seeing in on Wednesday. After the trip this school is on top of the list. I'll post up a couple pics from my phone.
 
This is the cathedral building, it was completed in 1938 and is reminiscent of the Empire state building completed in 31. It amazes me that this is a school building.

2016-03-30 19.52.05.jpg


Next up is Litchfield Toweres. These were built in the 60 s and remind me of the Marina Towers in Chicago, both of which were built in the 60 s.
20160330_134740.jpg
 
You must log in or register to reply here.
Back
Top Bottom