Friday, October 5, 2012

Your Puzzle Challenge - the Hula-Hoop Bag

Aside from the Presidential Debates a Spring 2013 Fashion show is going on in Paris these days.  There are many terrific, beautiful (and mathematical) new ideas.  One of them particularly caught my fancy. It is a Hula-hoop bag by Chanel. Finally - a bag that is easy to hold and play with, a bag that can be a beach bag, a work bag and a baby stuff bag in the same time. It may be a bit hard to squeeze in the bus or a car but you can hang it and hula-hoop plastic is a bit flexible. I just love it.  

This week I want to try something different. Instead of me posting a puzzle for you, I am doing a puzzle challenge. Can you create a puzzle about this bag? Anything that has at least a bit of math goes. Simple or hard.  Be creative!  

Image from NYTimes.

You have almost three days till Monday morning.  Post your ideas on our Family Puzzle Marathon


Wang said...

If we want the bag to carry, say, 2.25*pi m^3 and the hoop has a width of 0.5 m, how big does the hoop have to be (diameter) to support this kind of bag?

Anonymous said...

I looked on line to find out more about this purse. It is actually made with 2 hula hoops. If one were to make a purse like this, how much material would cover the surface are that you can see. This does not include lining or seams since I am a guy and would have no idea how much to allow. I saw on line that a hula hoop is about 28" in diameter. I think I can get a pretty good estimate of the bottom. The flap is tricky and needs someone smarter than I am to figure out the size of the flap. The top is held together with black duct tape holding the 2 hula hoops together. The very bottom looks to be about 6" but the sides taper until they meet the top flap half way up the hoop. Here is a diagram.
Maria, you did not say we have to figure the answer. Here is as far as i got. I estimated that the top of the purse itself was also the diameter or 28". That would be 615.44 sq. in. for one side It would be the same on the back also or 1230.88 for both sides2592.64.. I figured that there were basically 2 triangles to make the bottom. 2 triangles make a rectangle so it would be 6" on one side and the 2 other sides of the triangle are 87.92 but since we are using a rectangle then one fourth of the perimeter is the side and that is 21.98 in.times 6" and that is 131.88. I am not exactly sure how to figure out the flap. I figure it is about a quarter of the radius and somehow you need to divide this into triangles to get an exact answer. I think there is a formula for this though. My answer minus the flap is 2592.64.


Jerome said...

Observation 1
The girl is holding the bag in such a way that she is tilting it back with her hand. I think if she let it go, her elbow would pretty much hit the center of the hoop which is the top center of the bag. In other words the maximum width of the bag is the diameter of the hoola hoop.

Question 1. What is the diameter and circumference of the bag?

According to this reference, the distance from the acromion to the elbow (using the 50th % tile) is 335 mm in the United States. That makes the diameter 670 mm (26 and 3/8”) and the circumference 82” and 15/16 very approximately.

Observation 2
The girl’s elbow to her palm is roughly the same radius.

Question 2
What is the girl’s height? According to this article, it is 1/5 of a man from the elbow to the middle finger. Therefore we could use the estimate of 335 mm and multiply by 5 to give us 66 inches which is 5’ 6 inches tall which is likely a good estimate.

The reference by the way is to da Vinci’s very famous drawing of the Vitruvian Man which is related to the golden mean or phi.

Observation 3
The purse is pushed back by the palm and the center of gravity is on a line that if the girl let go, would be in the middle of the purse. Since she pushing it back with so little effort (especially since her hand is so close to the balance point of the purse) there is little or nothing in the purse and it is extremely light.

Question 3
Have I drawn the right conclusion? Anyone else want to guess at the weight of the purse. It couldn’t be any more than 3 pounds at the center of mass; otherwise she couldn’t move it given the diameter and the distance of the center of mass to the balance point on her shoulder and her hand which is moving the purse off the center of mass.

On the other hand, I guess it is possible that she has a whole mountain of stuff in her purse – all at the front.

Observation 4
Really just a question. I wonder what formula could be used for the hoola hoop/purse to calculate its moment of inertia. I won’t even begin to guess at this one, but I wonder if it is between a disk and a ring rolling down an incline.

Observation 5
I wonder if any of the ladies in the crowd could tell me how anyone could walk with such high heels, go straight and balance a purse like that on her shoulder without the hoop falling off her shoulder, or am I just being a guy with too much time on my hands?

Ilya said...

Alice owns a boutique handbag factory. She got a trial order from Chanel to produce an ingeniously designed bag that is built around a hula-hoop as a frame, as seen in the picture. The top of the bag’s fold is a line that’s passing through the center of the hoop. The hoop’s diameter is 2 feet, flap goes down half way (1 foot), following the circular shape of the hoop. The bag is 2 inches thick, with the cylindrically shaped “bottom” piece stitched between the two sides and attached to the hoop. Assuming all of the bag pouch’s exterior is made from the same material, and the material can be used very efficiently with scraps being stitched together as needed, how many square feet of this material should Alice order per each bag?

Bonus question: if you take this handbag to apple-picking, how many apples can you reasonably fit there without destroying the bag?

Jerome said...

I forgot the reference to my first observation question

Maria said...

You guys are terrific. I think each deserves a puzzle point for each idea, and another puzzle point if he provided an answer for the idea.

Wang - 1 puzzle point.
Gurubandhu - 2 puzzle points (for puzzle+answer, and I specially like the how-to-make-this-bag link)
Jerome - wow, seems like at least 8 points. In regards to your Observation 5: yes, we ladies are amazingly capable. Do you remember an old Coen brothers (?) movie where in the opening scenes we see a woman in the trailer park, holding a baby one hand, hanging her laundry with another and simultaneously answering a sex phone call in a headset?
Ilya - 2 puzzle points.

My fascination with this bag continues as see that it seems to naturally come out of the Chanel's logo - two overlapping almost-circles. Just like two hula-hoops supporting the bag.

The ideas that came to my mind are:
First simple question is whether the amount of leather that went to make this bag is larger than the area of the circle created by the hula-hoop. The answer is simple as bag seem to take exactly half of the hula-hoop circle. Therefore, front and back sides of the bag together make a perfect circle, but the top cover with the buckle demand more leather. But if you alter the design a bit removing the front flap and adding a wide zipper along the diameter, then you bag can consist of just two half-circle leather pieces.

Second question is how many ways you can hold this bag. On a shoulder as the model, hanging from an elbow, on a shoulder but criss-cross, going above your chest if you are skinny, in your hand hanging down - only if your heels are sufficiently high.

Another question: assuming that the diameter of the hula-hoop is 1 meter, what is the largest laptop size you can fit inside. There are should be few answers depending on the laptop's aspect ratio.

Maria said...

Wang and Jerome - you have reached a 50 puzzle point peak and I will be honored to interview you. Please get in touch via email

Maria said...

Jerome wrote to me that his wife Mary had an interesting thought about this bag:

" She wondered (she shared this one with me) if you made a miniature Hula Hoop purse for the baby carriage wheel-less puzzle a few weeks back how fast you would have to push the carriage so the “purse” attached to wheel (very miniature) wouldn’t spill its contents."

Abacus said...

If the height of girl is 6.3' and the radius of the bag is 15 cm, then

1. What is the weight of the girl?

2. In which category the girl falls?

3. What is the logic to calculate weight?

Abacus said...

I will submit my logic and answers after seeing some of the replies...

Sorry to forgot this in last reply so making this new one. So please publish it so people may can come and take interest in solving the puzzle.

Trust me its fun.....

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