My Math Forum  

Go Back   My Math Forum > College Math Forum > Topology

Topology Topology Math Forum

LinkBack Thread Tools Display Modes
January 28th, 2015, 04:25 PM   #1
Joined: Jan 2015
From: WA

Posts: 3
Thanks: 0

Question reposted: sewing conundrum concerning cones

Accidentally posted this in high school geometry first. Yeah, I think this is way out of their league.

So after some research (i.e., googling "what is topology") I figured it's better suited for ths forum instead.

made some pics to explain a bit better...

so, I'm making a costume, and I need to make a dress that's shaped like a cone. I have the materials to make a rigid hoop to sew into the bottom hem to weigh it down and hold a circular shape, but I don't know how to make the cone itself.

the basic shape has to be a circle with a wedge cut out, but there are a few stipulations.

the inner circle needs to have a final circumference of 40 inches, meaning afterthe edges of the wedge are sewn back together, the circle cut out of the middle needs to be 40 inches around.

the distance between the inner circle and the outer circle (the hem) needs to be 24 inches.

basically, these are the measurements I need:
  1. new inner circumference (BEFORE CUTTING AND SEWING)
  2. new outer diameter (BEFORE CUTTING/SEWING)
  3. wedge width (how much I need to cut out to form the cone)

hopefully this makes some sense... I'm totally lost here.
To clarify a bit, I'm not looking for an explanation of how to do it. I just want the answers. This is a personal project, not some college exam. I'm just at a total roadblock in my costume-making project and I'd like to get moving again.
thewitchmaker is offline  
January 29th, 2015, 06:06 AM   #2
Global Moderator
CRGreathouse's Avatar
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
This isn't really topology, but I'll answer it here rather than shuffle it around further.

Let's say the angle of the sector you cut out is $\alpha.$ Then the circumference of the new inner circle is the circumference of the original inner circle (let's call it C) times $1-\frac{\alpha}{2\pi}$. Setting that equal to 40 we get $C=\frac{40}{1-\frac{\alpha}{2\pi}}$ or $r=\frac{40}{2\pi-\alpha}.$

Now the radius of the large circle is 24 more, or $\frac{40}{2\pi-\alpha}+24.$ This makes the (original) outer circumference $\frac{80\pi}{2\pi-\alpha}+48\pi.$ You'll then cut out the same angle from it, making the new outer circumference

I'm not sure how you want to measure the wedge width. The 'missing' outer circumference is
and the 'missing' inner circumference is

If you prefer to measure in degrees, replace $\pi$ with $180^\circ.$
CRGreathouse is offline  

  My Math Forum > College Math Forum > Topology

cones, conundrum, reposted, sewing

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
sewing conundrum concerning cones thewitchmaker Geometry 1 January 28th, 2015 04:19 PM
Probability conundrum floodric Probability and Statistics 4 February 24th, 2014 10:01 AM
intersection of two cones white_flag Algebra 2 July 30th, 2012 06:46 AM
A conundrum.... random_thinker Applied Math 2 June 25th, 2009 04:41 AM
Polynomials and Cones AdamL12 Abstract Algebra 9 November 15th, 2007 01:44 PM

Copyright © 2019 My Math Forum. All rights reserved.