Interesting Math Problems

[QillerDaemon]

I don't know why I'm trying, but here's another interesting problem:

When a conical bottle rests on its flat base, the water in the bottle is 8 units from its vertex.

When the same bottle is turned upside-down (180 deg), the water level is 2 units from its base.

What is the height of the bottle from base to vertex. Clue: obviously the volume of water does not change.

[Burn1dwn]

I don't know why I'm trying, but here's another interesting problem:

I went through Calculus 2 in school and I can't even begin to try and solve these. I guess math isn't like riding a bike.

[Reservoir Dog]

10 units.

[CentralTexasCrude]

"For the Love of all that is Holy", don't get RD involved in a math question.

[QillerDaemon]

I don't know why I'm trying, but here's another interesting problem:

I went through Calculus 2 in school and I can't even begin to try and solve these. I guess math isn't like riding a bike.

I always wanted to study math in college, but there was something in my chain of thinking that didn't jibe with what it took to study down deep into mathematics. I had a few friends who were math majors, and this sort of stuff would have been child's play for them. On the other hand, I was a (bio)chemistry major, and they couldn't really handle chemistry's weird and wonderful irregularities. But here it is almost forty years later, and I keep trying to understand and enjoy math.

The solution is to regard each position (base up vs base down) as a difference of two similar triangles, so two sets of similar triangles. The smaller triangle of each set of similar triangles correlates with the volume of the water. Since that doesn't change, the smaller triangle of each set are equal in area, which directly leads to the solution. In this case, the height of the cone is 10.2, not 10 (sorry RD, no points). Nothing but simple algebra and the Pythagorean theorem, no calculus involved. Supposedly this was a problem presented to 15yo students in India.

[Reservoir Dog]

"For the Love of all that is Holy", don't get RD involved in a math question.

There you go with the math thing again. Are you ever going to get around to explaining what the hell you're talking about? Because I have no idea what the fuck you're talking about.
I've asked you on numerous occasions to explain it but you won't. I think you won't explain it because you can't explain it. It's just some typical, made-up, fantasy W/CTC bullshit. Just like most of your posts.

[Reservoir Dog]

I don't know why I'm trying, but here's another interesting problem:

I went through Calculus 2 in school and I can't even begin to try and solve these. I guess math isn't like riding a bike.

I always wanted to study math in college, but there was something in my chain of thinking that didn't jibe with what it took to study down deep into mathematics. I had a few friends who were math majors, and this sort of stuff would have been child's play for them. On the other hand, I was a (bio)chemistry major, and they couldn't really handle chemistry's weird and wonderful irregularities. But here it is almost forty years later, and I keep trying to understand and enjoy math.

The solution is to regard each position (base up vs base down) as a difference of two similar triangles, so two sets of similar triangles. The smaller triangle of each set of similar triangles correlates with the volume of the water. Since that doesn't change, the smaller triangle of each set are equal in area, which directly leads to the solution. In this case, the height of the cone is 10.2, not 10 (sorry RD, no points). Nothing but simple algebra and the Pythagorean theorem, no calculus involved. Supposedly this was a problem presented to 15yo students in India.

.2!... .2!... MY KINGDOM FOR A .2!

[Burn1dwn]

On the other hand, I was a (bio)chemistry major, and they couldn't handle chemistry's weird and wonderful irregularities. But here it is almost forty years later, and I keep trying to understand and enjoy math.

This makes a lot of sense to me.

I gave up my dreams of majoring in Geology after I dropped my first Chemistry course because I could not get sig figs down. One of my life's big regrets was not hiring a Chemistry tutor and sticking it out.

I never needed a math tutor before reading your thread.

[rule34]

I own tape measures, rulers, micrometers, dial indicators, calipers and many other measuring insturments for a reason.

[CentralTexasCrude]

"For the Love of all that is Holy", don't get RD involved in a math question.

There you go with the math thing again. Are you ever going to get around to explaining what the hell you're talking about? Because I have no idea what the fuck you're talking about.
I've asked you on numerous occasions to explain it but you won't. I think you won't explain it because you can't explain it. It's just some typical, made-up, fantasy W/CTC bullshit. Just like most of your posts.

Pure total BS. It happened 5 years ago and you know exactly what I'm talking about. Several people have asked for an explanation over the years, and we've both supplied our side of the story. So, save me the fake innocent BS routine and just own it- you could have admitted you were wrong way back then and saved a lot of trouble and you refused. See, I never forget.

[Reservoir Dog]

"For the Love of all that is Holy", don't get RD involved in a math question.

There you go with the math thing again. Are you ever going to get around to explaining what the hell you're talking about? Because I have no idea what the fuck you're talking about.
I've asked you on numerous occasions to explain it but you won't. I think you won't explain it because you can't explain it. It's just some typical, made-up, fantasy W/CTC bullshit. Just like most of your posts.

Pure total BS. It happened 5 years ago and you know exactly what I'm talking about. Several people have asked for an explanation over the years, and we've both supplied our side of the story. So, save me the fake innocent BS routine and just own it- you could have admitted you were wrong way back then and saved a lot of trouble and you refused. See, I never forget.

Nice empty runaround explaining nothing.
I was right. You can't explain it.

[CentralTexasCrude]

"For the Love of all that is Holy", don't get RD involved in a math question.

There you go with the math thing again. Are you ever going to get around to explaining what the hell you're talking about? Because I have no idea what the fuck you're talking about.
I've asked you on numerous occasions to explain it but you won't. I think you won't explain it because you can't explain it. It's just some typical, made-up, fantasy W/CTC bullshit. Just like most of your posts.

Pure total BS. It happened 5 years ago and you know exactly what I'm talking about. Several people have asked for an explanation over the years, and we've both supplied our side of the story. So, save me the fake innocent BS routine and just own it- you could have admitted you were wrong way back then and saved a lot of trouble and you refused. See, I never forget.

Nice empty runaround explaining nothing.
I was right. You can't explain it.

Total utter BS. Could have ended it 5 years ago with a few simple words. You compounded it by doubling down 2 years ago. You have no one to blame but yourself and I will hound you forever. Promise.

[CaptQuint]

FINGERS HOVERING OVER THE KEYBOARD AHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAH

[Reservoir Dog]

"For the Love of all that is Holy", don't get RD involved in a math question.

There you go with the math thing again. Are you ever going to get around to explaining what the hell you're talking about? Because I have no idea what the fuck you're talking about.
I've asked you on numerous occasions to explain it but you won't. I think you won't explain it because you can't explain it. It's just some typical, made-up, fantasy W/CTC bullshit. Just like most of your posts.

Pure total BS. It happened 5 years ago and you know exactly what I'm talking about. Several people have asked for an explanation over the years, and we've both supplied our side of the story. So, save me the fake innocent BS routine and just own it- you could have admitted you were wrong way back then and saved a lot of trouble and you refused. See, I never forget.

Nice empty runaround explaining nothing.
I was right. You can't explain it.

Total utter BS. Could have ended it 5 years ago with a few simple words. You compounded it by doubling down 2 years ago. You have no one to blame but yourself and I will hound you forever. Promise.

Yet again you can't answer.

What math?

Seriously, what do you find so hard about answering one simple little question? It's almost as if you're completely full of shit or something. You talk a lot but you answer nothing.

What math?

[Animal]

New problem:

A square is cut up into five rectangles of equal area. The rectangles will not necessarily have the same dimensions. The side length of one rectangle is four units. How many units is the original square? The answer is a number, not a formula.

I am not going to read down, in case anyone has posted the answer. Let me think about this.

My first guess would be that the Original Square is 5 units x 5 units.

Four of the rectangles would be 4x1 and the fifth rectangle would be 2x2. All having an area of 4 units.

[megman]

Has 42 been mentioned?

[CentralTexasCrude]

New problem:

A square is cut up into five rectangles of equal area. The rectangles will not necessarily have the same dimensions. The side length of one rectangle is four units. How many units is the original square? The answer is a number, not a formula.

I am not going to read down, in case anyone has posted the answer. Let me think about this.

My first guess would be that the Original Square is 5 units x 5 units.

Four of the rectangles would be 4x1 and the fifth rectangle would be 2x2. All having an area of 4 units.

Sounds like you are on the right path. Just don't get RD involved. The math all goes to shit.

[Animal]

New problem:

A square is cut up into five rectangles of equal area. The rectangles will not necessarily have the same dimensions. The side length of one rectangle is four units. How many units is the original square? The answer is a number, not a formula.

I am not going to read down, in case anyone has posted the answer. Let me think about this.

My first guess would be that the Original Square is 5 units x 5 units.

Four of the rectangles would be 4x1 and the fifth rectangle would be 2x2. All having an area of 4 units.

Sounds like you are on the right path. Just don't get RD involved. The math all goes to shit.

i'm locking that answer in.

[CaptQuint]

Just don't bring Supreme Court decisions into it, they make the texas tards head spin

[Animal]

10 units.

It seems like this answer would work as well. You could have 2 rectangles that are 5x4 and then 3 that are 10x2. The area of each of the rectangles in this example is 20 square units. The Square it all started from was 10 units x 10 units. I suspect there are infinite solutions to this problem.

[megman]

What. What? I thought it was triangles...

[QillerDaemon]

New problem:

A square is cut up into five rectangles of equal area. The rectangles will not necessarily have the same dimensions. The side length of one rectangle is four units. How many units is the original square? The answer is a number, not a formula.

I am not going to read down, in case anyone has posted the answer. Let me think about this.

My first guess would be that the Original Square is 5 units x 5 units.

Four of the rectangles would be 4x1 and the fifth rectangle would be 2x2. All having an area of 4 units.

I kinda regret asking this problem now, only because you have to know there is only one way to cut up a square into five rectangles and have them all have the same area, *and* have one of the rectangles having a side length of 4 units at the same time. In cutting up the square, it turns out that there's a smaller square made up of three of the equal-area rectangles, and from there it's simple math. The side length of the original square turns out to be 16 units, with total area 256 units.

You can cut up a square in all sorts of ways that involve the component rectangles having equal areas and with each rectangle having its own dimensions. But only one way to do it such that one rectangle has a side length of four. I thought that was obvious, but it really isn't.

[Animal]

New problem:

A square is cut up into five rectangles of equal area. The rectangles will not necessarily have the same dimensions. The side length of one rectangle is four units. How many units is the original square? The answer is a number, not a formula.

I am not going to read down, in case anyone has posted the answer. Let me think about this.

My first guess would be that the Original Square is 5 units x 5 units.

Four of the rectangles would be 4x1 and the fifth rectangle would be 2x2. All having an area of 4 units.

I kinda regret asking this problem now, only because you have to know there is only one way to cut up a square into five rectangles and have them all have the same area, *and* have one of the rectangles having a side length of 4 units at the same time. In cutting up the square, it turns out that there's a smaller square made up of three of the equal-area rectangles, and from there it's simple math. The side length of the original square turns out to be 16 units, with total area 256 units.

You can cut up a square in all sorts of ways that involve the component rectangles having equal areas and with each rectangle having its own dimensions. But only one way to do it such that one rectangle has a side length of four. I thought that was obvious, but it really isn't.

i'm not sure i'm following this. Are you saying that the trick to the question is that ONLY one of the 5 rectangles can have a side equal to 4?

[Animal]

and you are wrong if you think there is only one way to cut up a square into 5 rectangles and have them all be of equal area.

Think of a Square with sides of 10.

One one side of that square you cut out two rectangles that are 5 x 4 each. That leaves the square with 6 x 10. Which you cut into 3 rectangles that are each 2 x 10. Now you have 5 rectangles that are all 20 square units each all cut from that large square.

Now think of a square with sides of 5 units. You go around the edges and cut 4 rectangles that are each 4x1. That leaves a hole in the middle that is 2x2. Now you have 5 rectangles that are each 4 square units all cut from the large square. With a completely different cutting pattern.

[CentralTexasCrude]

What. What? I thought it was triangles...