"Recreational mathematics": an obvious oxymoron to most non-mathematicians, but a pleonasm to true believers.

*Mathematics after forty years of the space age.*(via curiosamathematica)

"Recreational mathematics": an obvious oxymoron to most non-mathematicians, but a pleonasm to true believers.

Solomon Golomb, *Mathematics after forty years of the space age.* (via curiosamathematica)

So basically if you take the sin of some shit, and divide it by precisely the same shit, the limit is 1.

Calculus professor (via mathprofessorquotes)

**Anonymous** asked:

hi... could you help me with something? what do those numbers and letters on a car's gear shift/stick mean?

Hello,

Sorry but I haven’t really got a good idea of what they are myself, I don’t drive and I never really paid too much attention to things like this.

I think though that the numbers are probably gears that increase the maximum cap of the speed the car can go at as the numbers increase. (This is a complete and utter guess.)

The letters, if I remember are: P, R, N, D, L

P - Park, used when you want to park the car I assume

R - Reverse, alters the rotation of the wheels so that the car moves backwards.

N - Neutral, not 100% what this means. Not even 5% sure what this means sorry.

D - Drive, also no idea what this means, sorry.

L - Low, I think this means that this is used when going up a hill? I don’t know.

I’m not much of a car person… Sorry

This one time I was at a party and there was a lamp that kind of did the thing so it looked like a tesseract (not the Avengers thing, the 4 dimensional object) and a friend pointed it out to me then challenged me to make a pick up line out of it.

So I grabbed the nearest girl, asked her to sit down with me and I said:

"Look at this, this is a 4 dimensional tesseract, only it’s not. It’s a 2 dimensional image frame that we are seeing of a 3 dimensional object in our 3 dimensional world, that perfectly illustrates one viewing angle of this regular 4 dimensional object. Isn’t that amazing? I think it’s pretty beautiful how something like this is possible, and it’s even more beautiful that even if we were to rotate the tesseract through the 4 dimensions, we could still have a representation of it one and two dimensions lower. I’m sure if we could see in 4 dimensions, that if we occupied a 4 dimensional world we’d be better equipped to witness the beauty of the tesseract, but even so this is still stunningly amazing, don’t you think?"

At this point she’s nodding, moderately impressed, so I looked her over and continued with:

"Hey, can I ask you something? Are you a tesseract?"

And I swear no one has ever or will ever laugh at me that hard ever again.

(I don’t even think half of what I said was accurate at all).

**ngeetee** asked:

How does Gabriel's horn have finite volume? Wouldnt the radius just get infinitely smaller but never reach zero?

ngeetee

Gabriel’s Horn has infinite length which is important because “at infinity” (a term that I have been told off multiple times for using but that I feel gets the point across nicely) the radius will have reached zero as it is continuously tending towards zero.

Using a bit of calculus we can calculate the volume of the horn which shows us that the horn has finite volume.

Gabriel’s Horn is a shape created by rotating the graph of y=1/x about the x-axis for x>= 1.

Imagine the bit of the graph of y=1/x and then rotating that through 360 degrees around the x-axis, such that it carves out a 3-dimensional object. This is Gabriel’s Horn.

From this we see that the radius of Gabriel’s Horn along the x-axis is equivalent to y, and hence r=1/x.

We can calculate the surface area and volume of Gabriel’s Horn by taking integrating between x=1 and infinity the expressions for the circumference and cross-sectional area of Gabriel’s Horn respectively. As the cross section is simply a circle at each point, the expressions required are 2πr and πr^2.

Hence the volume is given by π times the integral of y^2 = 1/(x^2) with respect to x from x=1 to infinity.

By taking the integral of 1/(x^2) with respect to x from x=1 to a, we see that the volume of Gabriel’s Horn between x=1 and a is (-1/a) – (-1/1) = 1 - 1/a = (a-1)/a. As a approaches infinity, (a-1)/a approaches 1 and thus the volume of Gabriel’s Horn is π*1 = π

The surface area is therefore given as 2π times the integral of y= 1/x with respect to x between x=1 and infinity.

Once more, taking the integral of 1/x with respect to x from x = 1 to x = a and tending a to infinity, we get ln(a) – ln(1) = ln(a). However, ln(x) is an increasing function, and so as a tends to infinity so does ln(a), meaning that the surface area of Gabriel’s Horn is infinite.

And so we have that the surface area of Gabriel’s Horn is infinite, whereas the volume is finite.

Hope this has helped clear things up! Have a nice day.