Origami Chopstick Rest: UPDATE 1

January 10th, 2010 Mr. H 2 comments

Here’s the update to Origami Chopstick Rest that I mentioned earlier (click on the link to get to the pics).

I tried following some of the tips on (PDF) Origami Diagramming Conventions: A Historical Perspective by Robert Lang.

This is what I have so far.

One problem I’m having is how to diagram the last step where I create a saddle like shape from the straight edge.

It is not the standard straight line fold. A quick search and image search for origami, origami notation, origami diagram didn’t yield what I was looking for; most examples were of straight line folds.

Any origamist or origami diagramist (is that a word?) know how to show that in a diagram?

Origami Chopstick Rest

December 30th, 2009 Mr. H No comments

Have you ever touched the table surfaces at your local Chinese restaurant? There’s a reason why they invented the chopstick rest.

You don’t have to buy one can carry it around with you. Next time you’re waiting the 10-20 minutes for your food, take your paper chopstick wrapper and make an origami chopstick rest.

Here’s a sample:

Many chopstick wrappers are open on one end. However, some wrappers may cover the chopsticks completely.

It may be necessary to rip open one of the ends. You can tear it off completely. I choose to leave it on (no bits of paper to throw away).

Fold the wrapper in half.

Fold it again in half.

This next step is optional. I re-fold so that there’s no hanging torn bits on the outside.

Fold in half along the length.

Fold triangularly along one of the corners.

Do the same for all 4 corners.

Fold them together and you get.

At this point you can stop. You’ve just created a simple chopstick rest that’s fairly functional. The first time you try this you may find the food arriving on your table when you finish. As you become more adept and folding them, you may want to modify this base to create fancier and in some cases more functional chopstick rest. I’ll give an example below.

You may notice that the above chopstick rest may rock back and forth. The middle support section is a little longer than the sides. One way to fix this is to fold the middle support section.

Do it again for the other side and you have a more stable chopstick rest.

One last thing about this rest is that it is straight along its length and the chopstick may slide off the sides. To avoid this, we can create a saddle, a slight curvature down the middle like the real chopstick rests.

Here’s the final rest in action:

I’ll probably update it later with instructions in traditional origami notation.

URL Shortener Math

December 21st, 2009 Mr. H No comments

So you might have gotten wind that I started tweeting. I’m trying to think of ways of using it productively or at least I’m trying to justify the amount of time I spend on it to myself.

So far I’ve met some very knowledgeable folks and had some interesting conversations (as much as 140 characters will allow). Meaningful conversations can be hard on Twitter. Maybe one day I’ll learn to be more effective with words and to communicate with more precision while using less words. For now, I am using Twitter more for link discovery than anything else. I’ve retweeted some interesting links and I’ve noticed that just about everyone uses an URL shortener.

I’ve never been particularly fond of an URL shortener. Jeff Atwood at Coding Horror has expressed some of my thoughts better on Url Shorteners: Destroying the Web Since 2002, but that’s a whole other post there.

So far I am aware of about 4 URL shortener services frequently used on Twitter. They are:

Bit.ly is the first one that I used. One nice benefit of the service is that you can see the number of times that people have clicked on your link. You can even see the number of clicks from your shortened link compared the the number of total clicks on other shortened links to that same URL. No other service on my list seems to provide this information. But I digress.

I used the 4 URL shortener services to shorten this post’s URL: http://mrho.net/blog/?p=868. There results are below.


Bit.ly produced http://bit.ly/7hFVX7. Seems like it uses 6 upper case, lower case, and number (alphanumeric character) combination to uniquely identify a link. Whether not they will increase to 7 alphanumeric characters when 6 runs out is unknown. Re-entering the same link into the service produces the same shortened link.


The next service is Ow.ly. One nice “feature” of this service is that it uses one less letter in it name than Bit.ly.

The service produced http://ow.ly/Otn1 for this post’s URL. It seems the service uses only 4 upper case, lower case, and number combination to uniquely identify a link. Re-entering the same link into the services produces a different shortened link in a predictable order. This is an interesting “feature” especially for a math class. Some additional testing and we can see the minimum number of alphanumeric characters it will take is 3.


The next service is Im.ly

The service produced http://im.ly/b1fc5/. It seems to use only 5 lower case, and number combination to uniquely identify a link. Re-entering the same link produces the same shortened URL.


Lastly is Is.gd

The service produced http://is.gd/5wSXx. Relatively speaking, it has the more spartan interface of the services in this list. The service uses 5 upper case, lower case, and number combination to uniquely identify a link. Entering the same link again produces the same shortened URL.


Summary of URL Shortener Services
Service ID Length Upper Case Lower Case Numbers
bit.ly 6 Y Y Y
ow.ly 4 (so far) Y Y Y
im.ly 5 N Y Y
is.gd 5 Y Y Y

Questions to students:

  • Which is the best service? (how do you define best?)
  • Which service would you use and why?
  • Which service can hold the most links?
  • Can we tell how many links are stored in the service as of now? If so how many? (hint: Ow.ly is the only one)
  • How many more links needs to be shortened before Ow.ly needs 5 alphanumeric characters?
  • Can any service shorten the links to all the pages in the entire web?
  • Can any service shorten all the links in the entire web in 5, 10, 20, 50, 100 years? How can you find out? (assuming same rate of growth)
  • Is it OK to recycle links like we do with license plates? What are some potential issues? What happens if a service is gone?
  • How many unique links do we need to have to accommodate everyone in the world? What if we recycle the links?
  • Are there ways to maximize the number of links?
  • Could we use a word shortener to “increase” the information density in a single tweet?
  • If the alphanumeric characters represent a positional numeral system, what would be its base? What is one hundred/thousand/million/billion/trillion in this base? How does allowing or disallowing upper case and lower case change these numbers?

What other questions would you ask? How would you support students to answer some of the questions above?

UPDATE: A reader points out a WCYDWT (What Can You Do With This) series by Dan Meyer on license plates.

Twitter Newbie

December 10th, 2009 Mr. H 2 comments

It’s been about a week since I started tweeting. I’m not sure if there is a right way of using twitter and I haven’t found a very good use for it yet. I’ve been mostly looking around seeing what other people are sharing. Occasionally I’ll say something back, except I found out that simply hitting reply doesn’t actually reply to the original tweet. I can’t even send a direct message to a person who does not follow me back.

Interestingly, during this first week, the first few tweets that I read were of users in other countries complaining/wondering about spammers (me) following them. Typical comment is why would someone from a English speaking country follow me. If only I could tweet at them or direct message them.

If you use twitter and you follow this blog, please add me on twitter @mrhodotnet. I could use some helpful tips on using twitter productively or otherwise.

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Sampling and Response Bias (The Daily Show Edition) Part 2

November 26th, 2009 Mr. H No comments

In case you missed it, read Part 1 on Sampling and Response Bias and watch the video clip there first.

All the sample surveys from the clip use convenient sampling. There is no mention of any attempt to sample the US population properly to get an idea of what the general public opinion is on any issue. It is likely that there is undercoverage of segments of the population. The language used is usually “x percent of you” feel this way, which is technically correct in the sense that “you” represent the viewers who vote. One can easily get the impression of “you” representing the US population. To be fair, FOXNews (in the first clip) did qualify the statement on the first clip about the poll results with:

93% of you, who know how to text, say no! That we should not be talking to moderate factions of the Taliban

He would’ve been more accurate if he had said 93% of the votes (who knows if callers can vote more than once or whether the 93% who know how to text actually texted) on this poll which is most likely not representative of Americans or even the viewership of FOXNews (convenience samples are rarely representative) have voted NO (negative or strong emotions are typical of voluntary responders).

After the students identified voluntary response bias due to convenience sampling as a problem with all the clips, I asked students to change the wording of the questions so that they’re more neutral, or at the least, use words that are less emotionally charged. This was quite challenging since the textbook does not give examples or guidelines about how to reword the questions. Many students who don’t follow the news or read newspapers or magazine are unfamiliar with political correctness and did not see problems in the wording of questions. Some questions seemed neutral to the students. For most of the questions, they simplified the wording of the question but essentially the tone is similar.

Some of the more successful rewording and observations from students are:

Are you outraged that you are expected to tighten your belt and make tough choices, while Washington goes on a spending binge of historic proportions?

This question essentially is worded as “Are you outraged that you [have to suffer], while [somebody else doesn't]?” Even if we remove the more emotionally charged “tighten your belt” and “make tough choices” along with “spending binge of historic proportions” the sentence is still biased. Students offered “Do you agree with the amount of government spending?” Another student came up with “Do you think that the government should spend more or less to help the economy?”

Are you outraged that big business and socio-ethnocentric special interest groups are trying to destroy the most effective government program to fight illegal immigration?

Once again the question is worded as “Are you outraged that [bad people] and trying to destroy [something good that fights something bad]?” Even if “big business” and “socio-ethnocentric special interest groups”, “destroy the most effective government program”, and “fight illegal immigration” are replaced with more neutral terms the question serve no purpose other than to get people upset at certain groups. One student attempted “How do you feel about businesses and interest groups’ lack of support of immigration laws?” Another tried “Many businesses and special interest groups do not support the enforcement of immigration laws. Do you agree with that position?”

Do you believe it’s time illegal aliens said, “thank you” for all the help and support they get in this country, help and support they don’t get from the countries they’ve left?

Is there any point in asking this question? He might as well have asked “Do you believe [people should say "thank you"] for [all the nice things others do for them], [nice things that no one else would do for them]?” Students just gave up on trying to improve on this one.

Do we need a tax hike?

The way it’s worded is so general as to be meaningless. Most people will oppose tax hikes. In the context of the clip, it’s about providing health care to people who don’t have them. The least they could do is to mention what the tax hike revenue will be used for.

Is it fair to tax the [top] 1.2% of the richest Americans to pay for health care?

It’s basically asking whether the 98.8% of Americans should get a benefit paid for by people who have the most money and derive the most benefit from our economy. How would you vote?

All in all, students had a lot of fun watching the clips but struggled to come up with better and more neutral rewording of questions. They also got a pretty good idea about why most of these polls are bogus. First, the samples are not representative of Americans. Second, the wording of most questions suggest that the pollers are not interested in accurately measuring public opinion.

I was happy the next day when a student told me that she watched some of these news shows with her sister and they had a pretty good conversation about sampling and response bias. Students are learning. If you use this in your class, please let me know how you used it or what activities you did with it. I’d like to know about your experiences.

Lastly, a moment of Zen.

This last clip gives a good reason of why we should ignore internet or phone polls that were not sampled properly.

Sampling and Response Bias (The Daily Show Edition) Part 1
Sampling and Response Bias (The Daily Show Edition) Part 2

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