Random Thoughts....

Nabster

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If you're looking at my answer, I didn't round pi. I keep it in my calculator to however many dozen decimal places it keeps.
That's an important step, don't lose decimals or round until you're done, then you round off to the final number you get. Any rounding or converting you do before you're finished means your final answer gets more and more incorrect.

You are overcomplicating it. The formula for area of a circle as stated is pi times the radius squared. It doesn't matter what format the numbers are in- the formula works. For the area of a circle with a diameter of an inch, it's pi times the radius of .5 squared, .25 times pi, .25 times 3.14159265358979etc, nets you something along the lines of .785398163. Since you had .25 times pi, that's two decimal places, so it's safe to assume rounding your final number to two decimal places is sufficient. I might go with 3 decimals just because that third is a five and rounding to two would change the answer by 1/100th.
 
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flydiscovery

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I think all of these problems stemmed from me thinking a circle with a diameter of 1 inch should have an area of 1 inch or more.

I don't know why I was thinking that.

but I'm better now. that was a good 2 hour brain fart.

and yeah, I was using a shitty mobile phone calc at the time. I just used 3.14 for pi instead of the "real pi"
I just figured out what you're thinking of. The CIRCUMFERENCE of a circle must be greater than its diameter. You can't compare area and diameter. That's like comparing apples and spanners or something.

Actually, it's only 1,000. You must have rounded pi when you converted back and forth.
LOL. Nice. The picture was good though, showed my point a lot better than I managed.
 
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salle

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mm yeah I thought the picture was a good idea as I prefer geometry to be shown with pictures as much as with numbers. but apparently it made me captain bleeding obvious *pouts*
 

flydiscovery

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Well, I liked it on principle. It's absolutely amazing how many people don't understand what pi is (I'm no saying you necessarily Night_Hawk, just in general), mostly because they weren't taught it or because it was presented in such an obscure way at a developmentally inappropriate time. We're learning more and more now, younger and younger and some really basic (and frankly cool) ideas are dropped by the wayside. Kids are doing calculus at 16, but if you ask them to explain, derive, or approximate pi they think you're batty. I know I wasn't taught this. I had a Sunday school teacher of all people go off on some kind of math tangent once (tangent, har har) and show it to us. No idea why.
 

Nabster

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Well, I liked it on principle. It's absolutely amazing how many people don't understand what pi is (I'm no saying you necessarily Night_Hawk, just in general), mostly because they weren't taught it or because it was presented in such an obscure way at a developmentally inappropriate time. We're learning more and more now, younger and younger and some really basic (and frankly cool) ideas are dropped by the wayside. Kids are doing calculus at 16, but if you ask them to explain, derive, or approximate pi they think you're batty. I know I wasn't taught this. I had a Sunday school teacher of all people go off on some kind of math tangent once (tangent, har har) and show it to us. No idea why.
I had an excellent math teacher in elementary school who actually showed and taught us how things applied and how they were used. Sure at times teaching advanced algebra/precalc to 5th graders was a bit much, but she could explain everything and how and why it worked well enough that we understood it.
 

salle

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One amazing thing is how old pi is. The Egyptians had a pretty damn impressive approximation of it 7 000 years ago.
 

NecroJoe

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For me, pi was always taught as some sort of abstract "magic" figure. As if remembering symbol for pi was just easier than remembering decimals. We were never taught what it meant. it would be like learning that "dog" was the word for a dog, only through recognition; you had no idea how to read english.
 

flydiscovery

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For me, pi was always taught as some sort of abstract "magic" figure. As if remembering symbol for pi was just easier than remembering decimals. We were never taught what it meant. it would be like learning that "dog" was the word for a dog, only through recognition; you had no idea how to read english.
Disappointingly, this is how most of us are taught these days. That was definitely my experience. Pi was something you had to know, memorize, and accept, not understand.

And guess what's also coming back in style. Sight reading, which is exactly recognizing "dog" and knowing what it means without reading it. I saw a billion trillion layers of educational craziness when I was volunteering and subbing.
 

salle

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well the most fundamental way to describe ? is to say it's the constant of the relationship of the diameter of a circle to it's circumference. i.e. the circumference is 3.14 times bigger than the diameter.
 

thevictor390

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Well, I liked it on principle. It's absolutely amazing how many people don't understand what pi is (I'm no saying you necessarily Night_Hawk, just in general), mostly because they weren't taught it or because it was presented in such an obscure way at a developmentally inappropriate time. We're learning more and more now, younger and younger and some really basic (and frankly cool) ideas are dropped by the wayside. Kids are doing calculus at 16, but if you ask them to explain, derive, or approximate pi they think you're batty. I know I wasn't taught this. I had a Sunday school teacher of all people go off on some kind of math tangent once (tangent, har har) and show it to us. No idea why.
I had an AMAZING Geometry teacher in my Freshmen year. I maintained a 100% average for the first three quarters just because he was able to explain everything so clearly (and to be fair, I'm quite good at logic). Drawing is an absolute must when doing anything concerning shapes...

EDIT:
And guess what's also coming back in style. Sight reading, which is exactly recognizing "dog" and knowing what it means without reading it. I saw a billion trillion layers of educational craziness when I was volunteering and subbing.
I have no idea what you are talking about. Off to Wikipedia!

EDIT 2:
That didn't help...
 
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Topgearfanatic

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Sight reading is, I believe, seeing a picture of a dog and being able to know that it is a dog.
 

NecroJoe

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I don't think it's called sight-reading...that's really just used a music term...but I know what you are talking about...just can't remember its name.

edit: It's not seeing a picture of a dog. It's seeing the word "dog."

Let's say you can't read chinese, but you learned what the chinese character for "dog" is. You can identify that word, even though you don't really understand what the symbol really means. It's just simple recognition.
 
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Nabster

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I had an AMAZING Geometry teacher in my Freshmen year. I maintained a 100% average for the first three quarters just because he was able to explain everything so clearly (and to be fair, I'm quite good at logic). Drawing is an absolute must when doing anything concerning shapes...
Mmm.. high school geometry. I had a pretty good teacher there as well, but she had this annoying habit of drawing all her diagrams like this:



Drove me batty.
 

flydiscovery

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I don't think it's called sight-reading...that's really just used a music term...but I know what you are talking about...just can't remember its name.

edit: It's not seeing a picture of a dog. It's seeing the word "dog."

Let's say you can't read chinese, but you learned what the chinese character for "dog" is. You can identify that word, even though you don't really understand what the symbol really means. It's just simple recognition.
It's called sight reading now. Sight reading music is actually rather different and involves an understanding of what a dot in a spot means. Kids now are sent home with lists of "sight words" they have to be able to recognize. It's definitely seeing the word and recognizing it, as you described.
 

thevictor390

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So.... reading without knowing the alphabet? Is there a point to that? It would make writing quite difficult and typing worse :hmm: Sorry if I'm being thick-headed here.
 

Ladamaha

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So.... reading without knowing the alphabet? Is there a point to that? It would make writing quite difficult and typing worse :hmm: Sorry if I'm being thick-headed here.
I think the logic behind is that the kids know what things around them are called and they learn how they are written by connecting the picture to the combination of letters.

In other words. You know what a dog looks like and how to say it, now you know how it's written.
 

flydiscovery

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So.... reading without knowing the alphabet? Is there a point to that? It would make writing quite difficult and typing worse :hmm: Sorry if I'm being thick-headed here.
No, you aren't being thick headed at all. It's completely worlds apart from how you learned. It's supposed to be somewhat of a short cut, a way to read more before you can actually read. I've also seen it used heavily with older children who are either learning English as a second language or requiring marked remediation. It's difficult for me to explain because I'm not an educator (nor a learning theorist), and I don't fully understand it myself. It's supposed to go along with phonics but make reading faster and more fluid. :shrug:

You probably sight read to some point without realizing it. I know I do it with big medical/science/biology words where the phonetics are either unclear (many combinations of language roots all in one word) or pronouncing them is unnecessary. So I see a drug name and I recognize it, know what it is, what it does, and probably what the brand name is, but I can't pronounce it correctly. I've done it with words in Harry Potter too. See it, know it, understand it, can't "read" it.

This is going to be a BAD explaination because it's been years since I took cognitive psychology, but try to imagine this. Your eyes see the shape of some lines on a piece of paper that looks like CAT. Inside your brain the shape of these lines maps directly with the shape

Since you've seen that shape in your life you know that's a cat and therefor the lines on paper CAT must also read cat. Does that make any sense what so ever? It's kind of a crazy notion.
 
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thevictor390

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I guess that's kind of my point. There doesn't seem to be any other way to read. If you tried to sound every word out letter by letter.... that wouldn't work out too well. And I often notice spelling errors simply because the word "doesn't look right."

I think I am way too literal for this discussion...
 
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