Mathematics!!

[goodbye_farewell]

How about......

 

Given r² = x² + y², how could I mentally solve for r, given x and y?  (especially if x and y are quite a bit different)

 

For example, x = 15 and y = 5.25?

 

Just some fun.  

 

Mentally, I would tell my fingers which buttons to push on the calculator/keyboard

[Suzaqu]

How did I miss that there was a math party thread until now!? My undergrad was in math and physics, and my masters is in math (but they let me take some theoretical physics courses). 

 

 

 

How about......

 

Given r² = x² + y², how could I mentally solve for r, given x and y?  (especially if x and y are quite a bit different)

 

For example, x = 15 and y = 5.25?

 

Just some fun.  

 

If r²=x²+y², then just take the square root of both sides and get r=x+y, easy!

 

(Only joking, please don't shun me)

[Artinum]

If x is very very small, y will be nearly r. Are you looking for a means to come up with quick estimates? There isn't really a way to accurately work out r without doing the proper sums.

[Sam Ashen]

If x is very very small, y will be nearly r. Are you looking for a means to come up with quick estimates? There isn't really a way to accurately work out r without doing the proper sums.

 

Yes.  Quick estimate.  Now, what is your standard for "accurate?"  Also, what do you mean by "x is very, very small?"

 

As another example, say x=1 and y=2.  I doubt you consider x to be very, very small compared to y, but r would be closer to y than to x.  The next question is, by how much?

 

My quick guess would be 2.25.  Checking against my calculator, I missed by about 0.6%.  If I threw in another guess, like, "a little less than 2.25 - How about 2.24?"  Then I am off by about 0.2%.

 

So the big hint is:  What is the first derivative of r²?

[GoldLynx]

How did I miss that there was a math party thread until now!? My undergrad was in math and physics, and my masters is in math (but they let me take some theoretical physics courses). 

 

 

 

 

If r²=x²+y², then just take the square root of both sides and get r=x+y, easy!

 

(Only joking, please don't shun me)

 

You had me HORRIFIED for a second. Welcome to the club!

 

[GoldLynx]

Yes.  Quick estimate.  Now, what is your standard for "accurate?"  Also, what do you mean by "x is very, very small?"

 

As another example, say x=1 and y=2.  I doubt you consider x to be very, very small compared to y, but r would be closer to y than to x.  The next question is, by how much?

 

My quick guess would be 2.25.  Checking against my calculator, I missed by about 0.6%.  If I threw in another guess, like, "a little less than 2.25 - How about 2.24?"  Then I am off by about 0.2%.

 

So the big hint is:  What is the first derivative of r²?

 

Oh, these! Lol *flashback to Calc I*

[Suzaqu]

Anyone having any luck on the puzzle?

 

 

I'm caught up in dy/dr 's and messes of equations.  I'm probably trying to stick too close to analysis and not bringing in the approximation element soon enough.

[Sam Ashen]

Anyone having any luck on the puzzle?

 

 

I'm caught up in dy/dr 's and messes of equations.  I'm probably trying to stick too close to analysis and not bringing in the approximation element soon enough.

 

One part of it:

 

r² = y² + D

dr/dy = 2y

 

So r ~=~ y + D/2y

 

For example, square-root of 27:

27 = y² + D = 5² + 2

So SQRT(27) ~=~ 5 + 2/2/5 = 5.2

The number on my calculator is: 5.19615242271 and the approximation is within 0.08% in this case.

 

There is a better way to approximate, but not mentally.

[Burnet Bramblerose]

Woo, math party! I'm a student in a STEM community college program and I tutor college math. I tried to get an astronomy degree back in the day but I flunked out. Upper year calculus and quantum physics killed me. I like to say I never got a degree but I have about forty arcminutes.

[Artinum]

I have pi/180 of a radian. :-)

[Sam Ashen]

I have pi/180 of a radian. :-)

 

What do you have a pi/180 of a radian in?

[Artinum]

What do you have a pi/180 of a radian in?

 

Mathematics. What else?   

[Jarric]

Love this topic (what I understand of it!); was good at maths in college, but then never went on to uni so I'm a bit rusty. Gonna follow along for more.

 

Here's one I like:

 

Imagine you have a piece of string wrapped tightly around the earth (it's a long piece of string!). Now imagine you want to lift that string off the ground by 1m all the way round. You'd need a lot of extra string for that, right? After all, the earth's pretty big...

 

Actually, you would only need about 6.3m of extra string for the whole planet.

 

The length of the original piece of string is 2*pi*r, where r is the radius of the earth in meters. So if we lift the string 1m off the ground the radius from the center of the earth to the string = r+1,

therefore the new string length is 2*pi*(r+1)

=2*pi*r +2*pi*1

minus the original length of 2*pi*r and the extra string needed is 2*pi~6.3

[Sam Ashen]

Going way back.....

 

How about......

 

Given r² = x² + y², how could I mentally solve for r, given x and y?  (especially if x and y are quite a bit different)

 

For example, x = 15 and y = 5.25?

 

Just some fun.  

 

A. Which number is bigger?  15.

B. Ratio of bigger to smaller?  A little bit less than 3.

C. Two times that ratio?  A little bit less than 6.

D. Smaller number divided by the number from C?  More than 5/6 and less than 1.  How about 7/8?

E. Add the numbers from Steps A and D.  15.875.

 

The correct number, rounded to three decimal places, is 15.892, so I was off by 0.1%.

 

Just thought it was something fun to try and practice.

[Sam Ashen]

This one is a question for everybody, not a little puzzle.

 

This is on the subject of Juxtaposition and Order of Operations:

 

What I might write is:  1260*15/3/(49.8)²

If I write:  1260*15/3(49.8)²

then I would insert a multiplication operation between the 3 and the (49.8)² and then resolve and get a different answer than the first line.

 

However.  I recently read an article that says the issue is currently not clear.

 

I also note the way I have this written by hand on a piece of paper in front of me, it is absolutely clear because I use a big horizontal line for division.

 

Yes the parenthesis are redundant.  I have a habit of doing that as a way to separate a number from an exponent - instead of 49.8².

[AugustaAdaByron]

The parentheses on the square are indeed redundant but I guess everything else could be resolved just by adding parentheses.

 

I'd read the first line as ((1260*15)/3)/(49.8)² and the second one as ((1260*15)/3)*(49.8)².

That being said I think the order is a matter of conventions.

[Artinum]

I get really irritated by those Facebook posts that give you something like "3 + 3 x 0 + 3" and say "95% of people get this wrong". I may have to introduce a blanket defriending policy on these people.

[Sam Ashen]

I get really irritated by those Facebook posts that give you something like "3 + 3 x 0 + 3" and say "95% of people get this wrong". I may have to introduce a blanket defriending policy on these people.

 

95% of people reading this statement believe the statement claiming 95% of people get this wrong and suddenly believe they are smart.

[Artinum]

Well exactly!

[caeliter]

86.3% of all made up stats contain the numeral 7... So I believe it, (I'm just playing the odds)