Optimizing Crease Length for a Folded Sheet of Paper

  • Thread starter fadi_nzr
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In summary, the conversation discusses how to fold a sheet of paper with dimensions 6 units by 25 units in a way that minimizes the length of the crease. A solution is proposed using proportions and the Pythagorean theorem, but it is questioned whether the crease should necessarily go through the top right hand corner. A more realistic sketch is suggested to better understand the problem.
  • #1
fadi_nzr
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You have a sheet of paper that is 6 units wide and 25 units long placed
so that the short side is facing you. Fold the lower right hand corner
over to touch the left side. Your task is to fold the paper in such a way
that the length of the crease is minimized. What is the length of the
crease?

this what I have attempted so far

15ckqqx.jpg


by proportions we get:

b/20 = a/sqrt(12a-36)

Solving for b. Use Pythagorean theorem to determine the length of c:

c^2 = a^2 + (36a^2)/(12a-36)

I am not sure if I am in the right track or not

any ideas or corrections
 
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  • #2
Your diagram seems to assume the crease will go through the top right hand corner. Why should that produce the minimum length?
 
  • #3
so how it should be
 
  • #4
Let it go through some arbitrary other point. And try to make the sketch a bit more realistic in terms of the length ratio (6:25).
 

FAQ: Optimizing Crease Length for a Folded Sheet of Paper

How can I prevent creases from forming on my clothes?

To minimize creases on your clothes, you can try the following tips:

  • Hang your clothes on hangers instead of folding them
  • Store your clothes in a cool, dry place
  • Avoid overstuffing your closet or dresser
  • Use fabric softener or dryer sheets when laundering
  • Iron or steam out any creases before wearing

What causes creases to form on clothes?

Creases on clothes are typically caused by pressure or friction. This can happen during storage, transportation, or wearing the clothes. Over time, these creases can become permanent if not addressed.

Can I remove creases from clothes that have already set in?

Yes, there are a few methods for removing creases from clothes that have already set in. You can try using a steamer, iron, or even a hairdryer on a low heat setting. Additionally, you can try dampening the creased area and then using heavy books or weights to flatten it out.

Are there any fabrics that are more prone to creasing?

Yes, some fabrics are more prone to creasing than others. Natural fabrics like cotton, linen, and silk tend to crease more easily, while synthetic fabrics like polyester and nylon are less likely to crease. However, this can also depend on the quality and weave of the fabric.

How can I minimize creases on delicate or special occasion garments?

If you have delicate or special occasion garments that are prone to creasing, you can try using a garment bag for storage or transportation. You can also consider investing in a clothes steamer, which is gentler on fabrics than an iron. Additionally, following the care instructions on the garment's label can help prevent creasing.

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