Maths Problem

UFOs, lost socks, discuss whatever you like here.

Moderators: Master_Kale, TNM Team

Post Reply
User avatar
Phasmatis
Off Topic Productions
Off Topic Productions
Posts: 2057
Joined: Sun Apr 25, 2004 7:55 am
Location: UK
Contact:

Maths Problem

Post by Phasmatis »

Hey guys, maths isn't my strong suit so I'm out sourcing this problem.

How would I find the length of the red line shown in this picture? I know the diameter is 512 so the radius is 256 but that's it.
Mathsproblem.jpg
Keeper of the pointy stick of injustice™.
bobby 55
Illuminati
Posts: 6354
Joined: Wed Jun 24, 2009 9:15 am
Location: Brisbane Australia

Re: Maths Problem

Post by bobby 55 »

Mathsproblem.jpg
Mathsproblem.jpg (31.47 KiB) Viewed 8238 times
Radius: Measure a to b; do the 2 pi r^2 thing. The tricky part is that arc (red line) isn't half a circle, but by approximating the degrees I think it's a third, so my totally amateur method would be measure a to b, do the 2 pi r^2 thing and divide by three.

So if that's the actual size, I measure a to b as 2.5 cm. Doing the 2 pi r^2 that gives a circumference of 15.7 cm. Using my half-assed approximation the line would be 5.23 cm in length. *throws science out the window*
Growing old is inevitable.......Growing up is optional
User avatar
Jaedar
Illuminati
Posts: 3937
Joined: Fri Mar 20, 2009 3:01 pm
Location: Terra, Sweden, Uppsala.

Re: Maths Problem

Post by Jaedar »

So there's 18 segments to make up a semicircle, that means each segment is pi/(2*18) radians, or 5 degrees. Since there's 5 segments missing on the left side, the angle of that segment is 13*5 degrees(or 13pi/36).

Next we'd like to know the radiues out to the red line, because then we can easily calculate its length=radians*radius. Sadly, I can't think of a way to get the radius to the red line without measuring in the picture or making some unfounded appeal to symmetry(ie the inner circles seems to split it in even radial three, so the red line should be at r/2 from the center.
"Delays are temporary; mediocrity is forever."
odio ergo sum
User avatar
Phasmatis
Off Topic Productions
Off Topic Productions
Posts: 2057
Joined: Sun Apr 25, 2004 7:55 am
Location: UK
Contact:

Re: Maths Problem

Post by Phasmatis »

Thanks guys, what I really need is the length of the missing section straightened out. So I guess I need to find the length of the longest edge.
Mathsproblem2.jpg
Hmmm, I think a better way for me to do this is to make a tube, this allows me to adjust the inner radius, outer radius and the angle so if I make a simpler shape...

The inner radius is 128, the outer radius is 256 and the angle is 90deg.
Mathsproblem3.jpg
If I do pi/90deg * 256, would that give me the circumference and so the circumference is the length of the longest edge? or am I way off?
Keeper of the pointy stick of injustice™.
G-Flex
Silhouette
Posts: 621
Joined: Mon Jul 11, 2011 10:16 pm

Re: Maths Problem

Post by G-Flex »

I have nooooo idea where you're getting that math from at the end, and for what it's worth, there's also no way in hell that arc is 90 degrees. This is easily viewed if you look at the picture rotated.

There are nine segments in the outer ring per 90 degrees, so 360 total, so 10 degrees per segment. The red arc cuts across exactly 13 of them; it's a 130-degree arc.

You don't use degrees in this kind of math because the number of degrees in a circle is totally arbitrary and meaningless. You convert to radian measure:

130/180 * pi = (13/18)pi

The arc length of the circle is just that angle times the radius, because the whole point of radians is that an angle in radians is the arc length of an arc with that angle with a radius of 1. So:

(13/18)pi * 256 = (3328/18)pi = (1664/9)pi ~= 580.85

Assuming, of course, the radius is 256. I could have misread something.
User avatar
Phasmatis
Off Topic Productions
Off Topic Productions
Posts: 2057
Joined: Sun Apr 25, 2004 7:55 am
Location: UK
Contact:

Re: Maths Problem

Post by Phasmatis »

Hahaha, that equation was a product of just waking up and not really thinking about it too much. The 90deg is for the second image as I thought that would be easier but this is all for a future problem I will have. Basically, I will be making some curved stairs, the best way to do that is to make a straight set of stairs and then bend them to the right angle. I need the length of the straight stairs so I know it will be the correct length when they are bent into shape.

I'm still a bit confused where does the 180 come from in this part?

130/180 * pi = (13/18)pi

Using my last image, the 90deg angle one, if I have this right... 90/180 * pi = (9/18)pi * 256 = 401.92 so that's the length I would use for the straight stair case.

Edit:
Right, with your help I knew what to search for on google and I now understand it a bit better. Using my last image. 90/180 * pi * 256 so divide 90 by a semi circle, times that by pi and then times that by the radius, this will get me the arc length, which should be the length of the straight stairs.

Thanks! You've been a great help.
Keeper of the pointy stick of injustice™.
G-Flex
Silhouette
Posts: 621
Joined: Mon Jul 11, 2011 10:16 pm

Re: Maths Problem

Post by G-Flex »

Phasmatis wrote:I'm still a bit confused where does the 180 come from in this part?

130/180 * pi = (13/18)pi
Converting degrees to radians, since (degrees / 180)pi = radians.
Post Reply