It’s the end of the semester, and I’m pretty much out of markers. So it’s time to order up some new ones. And hooray, they are on sale!

Well sort of.

Or maybe I’ll wait until the sale ends….

12 tables, 24 chairs, and plenty of chalk

It’s the end of the semester, and I’m pretty much out of markers. So it’s time to order up some new ones. And hooray, they are on sale!

Well sort of.

Or maybe I’ll wait until the sale ends….

Last month there was a story on BBC.com entitled “Spain’s new submarine ‘too big for its dock'” (https://www.bbc.com/news/world-europe-44871788)

The main part of the story is that Spain’s new non-nuclear submarines were built too large for their docks. (Hmmm. Guess that was obvious just from the headline.)

The reason the submarines were too large is that they were redesigned to be bigger than originally planned.

The reason they were designed to be bigger than originally planned is that they were heavier than expected, and so the buoyancy was off, which for submarines is pretty important. By the time that was discovered it was easier to increase the buoyancy by increasing the volume than by decreasing the weight.

And finally: The reason that they were so heavy is that someone put a decimal point in the wrong place. According to the article “Navantia gets US help to fix overweight sub” by T. Kington (from http://www.defensenews.com in June 2013, but apparently unavailable now), the former director of the Office of Strategic Assessment at Spain’s Defense Ministry, said **“I have been told it was a simple matter of someone writing in one zero when they should have written three.”** I put that in bold, because that small mistake, just twice zero, has taken years and ~~millions~~ billions of euros to (still not fully) rectify. The contracts for four subs were signed in 2004, the first of the subs was nearly done in 2012 when the mistake was discovered, and now it looks like the subs are all dressed up with nowhere to go. Poor subs – we look forward to a mathematically successful end to this story.

*The submarine photo isn’t actually an S-80: it’s a public domain photo of the USS Chicago (U.S. Navy Photo by Photographer’s Mate 1st Class Kevin H. Tierney. Edited by ed g2s). *

The verdict is in: despite my less-than-perfect cutting and decorating skills, a Sierpinski cake does indeed look pretty cool.

I had been so distracted by the descriptions of triangular cupcake liners that I didn’t order any, but certainly those would have made for more equally shaped triangles and a crisper looking design. This was made by baking a 9″×13″ cake, cutting it into 3 long strips, and doing a zigzag pattern on each to get 9 equilateralish triangles plus a bit extra. Now I just need an extra-large platter for serving, because we are SO having this again sometime…

I was just looking up triangular cupcake molds, as one does — or at least, as one does after the upcoming birthday child asks if their cake can be made into a Sierpinski triangle, and you both mull about it and then realize that that would be CRAZY because then no one would get any cake, and then you get distracted wondering if it could be approximated with cupcakes and you realize that would be awesome and the next time you make cupcakes they really should be displayed in a Sierpinski triangle — and upon looking at a couple pages of molds I noticed a funny thing.

Amazon has trouble with triangles.

Granted, I only saw oddities on two pages, but since that’s 100% of the pages I looked at, it was still a pretty high percentage.

**Exhibit #1: ** Triangle is now a color:

**Exhibit #2: ** Triangles have a diameter:

Of course, triangles do in fact have a diameter, since there’s a maximal distance between points (which turns out to be the length of the longest side). So presumably these are 2″ per side, and Amazon gets bonus points for an unnecessary use of Diameter. I admit, though, that part of me thinks that what they called “diameter” was really the distance from a vertex to the opposite side, because from a visual perspective I think that seems the most like the diameter of a circle. That would mean that the actual side length was (2/√3)*2″, or about 2.3″. The other cupcake liners were 2″ to a side at the base and 2.4″ to a side at the top, which means that either number would be consistent even if these were the same size.

So in the end, I’m not sure of the answer. What I am certain of, however, is that the Sierpinski approximation cupcake is an awesome idea, and should become a reality as soon as possible.

Is it better to fill up a gas take once a week for $80, or put in a quarter tank 4 times a week for $20 each time? That question does have two reasonable answers, depending in no small part on whether you have access to $80 or just to $20 at a time, but what isn’t in doubt is that four quarter-fill-ups at $20 each isn’t actually cheaper overall than one full-fill-up at $80. Or at least, that shouldn’t be in doubt.

There’s an article about it here, but it doesn’t lessen the confusion at all.

(The reference to the question of which is closer, the West Cost or the Moon, is a reference to a discussion from a year ago.)

It has been a while since we’ve seen a math mistake in the news, but a recent search turned up an old one that I’d never seen (Thanks TwoPi for pointing it out!) And the funny thing is, it’s not actually a mistake at all – the math is correct. And that’s the problem.

Back in November of 2007, the National Lottery in the United Kingdom had a new scratchoff ticket for their “Cool Cash” Lotto. The idea behind the game was the a person would scratch to reveal a specific temperature — say, 15º — and would then scratch to reveal three more temperatures. If any of these three numbers was lower than the Chosen Special one (15º in this example), then the person won a prize. Hooray!

But this was in the UK, which uses Celsius, and negative temperatures are pretty common in the winter. So the target temperature might be something like –7º, and the three additional temperatures might be –6º, –5º, and –4º. From a mathematically correct point of view, that’s not a winning ticket because all the numbers are above –7º. But people who focused on the numberals 6, 5, and 4, all of which are less than 7, thought they’d won.

It took but a day for this to become a problem, and after no small amount of confusion on the part of customers and shopkeepers, the tickets were pulled. They had lasted less than a week. Lottery we hardly knew ye.

*For more details, including a video, see the article in the Manchester Evening News:*

*https://www.manchestereveningnews.co.uk/news/greater-manchester-news/cool-cash-card-confusion-1009701*

The post about the math mistake in temperature conversation reminded me of a formula that a friend told me about (thanks DSD!). She was traveling abroad, and the guide she was with said that to convert Celsius to Fahrenheit people should use the formula:

**Double the Celsius, and subtract from it the amount obtained by moving the decimal place one unit to the left. Then add 32 to get the corresponding Fahrenheit.**

For example, with a temperature like 50°C, you’d double 50 to get 100, then from that subtract 10.0 to get 90. Finally, you’d add 32 to 90 to get 122°F.

This is equivalent to the formula

Temp in °F = (9/5) (Temp in °C) + 32.

In particular, if C is the temperature in Celsius, the description to double and the subtract that amount with the decimal place moved describes 2C – 0.1(2C), which is 1.8C, or 9/5C.

It does seem to me to be quicker to compute 9/5C by doubling C and subtracting a tenth of the result than to multiple by 9 and divide by 5 in some order. The conversion isn’t as quick as “Double and add 30″*, perhaps, but unlike that estimation it has the advantage of being exact.

*a formula that always brings to mind the movie *Strange Brew*

*The thermometer is by Bernard Gagnon – Own work, CC BY-SA 3.0. It has Centigrade rather than Celsius at the top, which I found interesting since I remember learning both terms in school*.

This mistake was printed almost a year ago, but it’s still relevant, and math mistakes never go out of style. This was posted by Richard Fuhr, who I believe is the original author.

The author was looking at an article about the Gobi desert in China, which read in part: “Temperatures may vary up to 95°F (35°C) in one day in the Gobi.” It also indicated that the average temperature in winter was -40°F (-40°C) and in the summer could be 122°F (50°C)

The -40°F being equal to -40°C is correct – it’s the only place the two temps have equal numerical designation, and I am a little sad that I’ve never gotten to experience it except in windchill form. The 122°F being equal to 50°C is also correct, and something I have exactly no desire to experience, although it’s still lower than the 129.2°F (54°C) recorded in Kuwait last month. Both of those conversations can be found by using one of the formulas

- Temp in °C = (5/9) (Temp in °F – 32)
- Temp in °F = (9/5) (Temp in °C) + 32.

The issue is that these are temperature readings, not changes in temperature. For a change in temperature, the 32 in either formula will disappear, leaving

- Δ°C = (5/9) (Δ°F )
- Δ°F = (9/5) (Δ°C)

This means that a **variation **of temperature of 95°F would actually correspond to a change of about 52.8°C, not 35°C. And a variation of 35°C would be a change of “only” 63°F, not 95°F. It’s not possible to tell mathematically whether the correct variation was 95°F (53°C) or 63°F (35°C), but looking through The Internet at temperature variations, it appears to me that although either one is possible, the printed variation was likely intended to be 35°C, not 95°F.

*The photo above is by Doron, with a Creative Commons license. Thanks to YG for bringing the original article to my attention!*

One of our alums (Thanks CJ!) sent a link this summer about how MATH was used in the design of the Alignment Optical Telescope in the Apollo Lunar Modules. I mean, yes, of course it was, but in particular an Archimedes Spiral — a spiral where the distance is increasing steadily, such as *r = θ* in polar coordinates — was used instead of a heavier piece of equipment. This is, I think, the first time I’ve seen a modern application of the Archimedes spiral.

The video is available below, and there is more info at NASA.

Today is 2/4/16 or 4/2/16, depending on where you live and how you write dates. Either way, it’s a great day because 2^{4}=16 and 4^{2}=16. There aren’t many days like that (although we are treated to two this year), so it’s worth taking a moment to celebrate.

Converting between units can be hard, as seen before (and before and before). Fortunately, food containers often include both English units and Metric units. Unfortunately, those two don’t always match. Take, for example, Producers Sour Cream. Their 32 oz container says it has 907 grams, which is about what you’d expect. The 16-ounce container has half has many. Not half of 907, but half of that again: in bold defiance of the laws of physics, it sports a mere 226 grams.

This mistake has apparently gone on for years. What’s equally strange is that the various nutrition sites that include information about this product also say 16 oz (226g) without comment. Because, as stated above, units are hard.

*Thanks to Philip Bailey for bringing this to our attention! And speaking of Math Mistakes, as I was, several of the mistakes listed in this very blog are published in the PRIMUS article “Math Mistakes that Make the News” by Yours Truly, which can be downloaded for free during the month of March (2015).*

Back in the 80s, there was a commercial for Faberge Organic Shampoo. And even if the shampoo doesn’t sound familiar, you might have heard of the ad (“…and they tell two friends…”)

Hey, it’s exponential functions! 1 friend tells 2 friends, those 2 friends tell 4 friends, those 4 friends tell 9 friends, those…wait, 9? Where did that come from? And then those 9(?) friends tell 16 people. So it almost works, except that after the photo of 2 people they decided to switch to perfect squares.

Fortunately, a later ad brings the whole thing to a halt before reaching 9:

Good job Faberge people – you skipped the 9! Of course, this one went straight from 1, 2, 4 to 16 before diving headlong into a grid of 24 people, so I’m not sure it was much of a mathematical improvement.

*Threesixty360…your source for commenting on 30 year old math mistakes that have already been well documented.*

In spherical geometry, the shortest-length curve between two points on the surface of the sphere turns out to be part of a Great Circle – an equator-line circle that cuts the sphere in half. So lines are circles, which is fun to share with philosophers. (Note – taxicab geometry provides that same amusement, where circles are squares.)

So a natural question, where “natural” means I never actually thought of it but wish I had, is What is the longest line along the surface of the earth that goes entirely through water? This would be the longest possible straight-line sailing distance, if you ignored all the physical aspects of sailing like wind and water currents. Fortunately, before I even thought of the question, someone had answered it. Behold!

This gif appears to be from a youtube video by Patrick Anderson of 2012 (here) which has the advantage of being a little slower.

So that raises the question of the longest straight-line distance through land. And here’s a guess at it: http://i.imgur.com/nbNfl.jpg and then another one https://sites.google.com/site/guybruneau/fun-stuff/longest-distance-on-land, although that second one it doesn’t quite look like part of a Great Circle so possibly the projection imposed a different geometry. Or possibly I have trouble visualizing projections of Great Circles, which is also possible because they are weird. (The cool kind of weird, of course.)

*Thanks CJ for sending me that gif, although now that I’m finding myself asking questions like “What line passes through the most countries?” I can tell that it’s going to keep me from my grading for longer than it should.*

Decimal points are small, and so easy to lose. And it appears that many of them were lost on FAFSA (Free Application for Federal Student Aid) forms, which is NOT a place that you would want incorrect data. According to an official document from July 18, people filling out the form were supposed to round monetary values to the nearest dollar, rather than using exact dollar-and-cents amounts. But some people put down cents anyway, and the computer didn’t alert them, or tell them there was a problem. No, it slyly accepted the amounts, and then threw all the decimal points in the trash, so [as the official memo said], and income that had been recorded as $5000.19 was suddenly interpreted as $500019, which is one heck of a sweet income and probably enough to disqualify you from most financial aid.

This didn’t happen with just a couple people, either – *The Wire* says that 200,000 people are likely to be affected. And because it’s more than just a couple, schools have to look at all those applications, every single one, to catch any errors. Those errors might be that people didn’t get aid who should, which is a bummer, but it could also mean that people got too much money. That doesn’t sound as bad initially, but the July 18 memo says, ” If such aid has already been disbursed the institution may need to change awards and return (or have the student return) any overawarded funds.” I can’t imagine that it will go over all that well for a school to tell someone to give back money that was promised, so I suspect this messiness will last a while.

*Hat tip to Yousuf for pointing out this article!*