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Current time: August 23, 2019, 9:07 am

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Here is an old geometry/measurement chestnut for you.
#1
Here is an old geometry/measurement chestnut for you.
Draw a quarter circle and label the center point C and the points on either end of its arc, A and B.

Let the length of the quarter circle's radius = 1 unit 

Now draw the circle with diameter AB, and label another point on this circle D such that point D is not inside the original quarter circle CAB.

Find the area of circle ABD outside of quarter circle CAB. Place answer inside hide tags and justify your result.
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#2
RE: Here is an old geometry/measurement chestnut for you.
42?

Big Grin
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#3
RE: Here is an old geometry/measurement chestnut for you.
(November 7, 2018 at 7:08 pm)ignoramus Wrote: 42?

Big Grin


Wait, does your approach rely on string theory?
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#4
RE: Here is an old geometry/measurement chestnut for you.
(November 7, 2018 at 6:43 pm)Whateverist Wrote: Draw a quarter circle and label the center point C and the points on either end of its arc, A and B.

Let the length of the quarter circle's radius = 1 unit 

Now draw the circle with diameter AB, and label another point on this circle D such that point D is not inside the original quarter circle CAB.

Find the area of circle ABD outside of quarter circle CAB.  Place answer inside hide tags and justify your result.

An old problem of Hipparchus.


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#5
RE: Here is an old geometry/measurement chestnut for you.
I have no idea how a circle can be defined by three points. I think this is what you're getting at.


"There remain four irreducible objections to religious faith: that it wholly misrepresents the origins of man and the cosmos, that because of this original error it manages to combine the maximum servility with the maximum of solipsism, that it is both the result and the cause of dangerous sexual repression, and that it is ultimately grounded on wish-thinking." ~Christopher Hitchens, god is not Great

PM me your email address to join the Slack chat! I'll give you a taco(or five) if you join! --->There's an app and everything!<---
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#6
RE: Here is an old geometry/measurement chestnut for you.
[Image: 2lzvk4.jpg]

(where's Rob when I need him!)

(Rob, it's a joke man, relax)
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#7
RE: Here is an old geometry/measurement chestnut for you.
(November 7, 2018 at 9:08 pm)polymath257 Wrote:
(November 7, 2018 at 6:43 pm)Whateverist Wrote: Draw a quarter circle and label the center point C and the points on either end of its arc, A and B.

Let the length of the quarter circle's radius = 1 unit 

Now draw the circle with diameter AB, and label another point on this circle D such that point D is not inside the original quarter circle CAB.

Find the area of circle ABD outside of quarter circle CAB.  Place answer inside hide tags and justify your result.

An old problem of Hipparchus.




Thanks for the Hipparchus reference.  I didn't know that and will have to look into who that was.  I don't recall where I encountered it but for whatever reason I woke up too early this morning thinking about it and had to recreate it.

I love the elegance of the solution though and how unlikely it seems when you consider the shape whose area we must find in itself.  Very satisfying I think.

(November 7, 2018 at 9:13 pm)SteelCurtain Wrote: I have no idea how a circle can be defined by three points. I think this is what you're getting at.




That is basically the figure we're interested in but the circle which includes the point A and B whose center is at C looks a little misshapen, almost as though you were trying to get point C on the circle as well.  It shouldn't be on the circle since it is the circle's center point.  So the shaded region should include only the crescent shape inside the half circle but outside the quarter circle.  Is that clear?  

Sorry I didn't provide an image.  I certainly provided it when I gave it to advanced middle schoolers but I was keen to see if I could give specific enough directions for the sophisticates we get around here.

I'll leave it there if that clarifies the picture for you so you can enjoy polishing it off.
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#8
RE: Here is an old geometry/measurement chestnut for you.
Still looking for the chestnut.
Sanity adjacent.


Angel





IMGUR 
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#9
RE: Here is an old geometry/measurement chestnut for you.
(November 7, 2018 at 11:44 pm)The Valkyrie Wrote: Still looking for the chestnut.


Is that a nipple reference?  Glad to know you're an officianado (sp?) too.  My wife isn't into boobs but she knows my tastes in girl butt and will point them out for me.
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#10
RE: Here is an old geometry/measurement chestnut for you.
My take-




Not convinced that point "D" is required.
I never thought I'd live long enough to become a grumpy old bastard. Here I am, killing it!
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