**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!*

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

]]>(from Brainfreeze Puzzles: Digits 1-9 in each row, column, and square, plus digits 31415926 in each block of pink)

and grab a beverage of your choice

and enjoy. Happy Pi Day!

]]>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).*

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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.*

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.*

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!*

When I asked that very question, TwoPi mentioned “surmounted” as another example of an English word that seems to be used exclusively in one context: to describe Norman Windows (a window in the shape of a rectangle surmounted by a semicircle). “surmountable” is more common, and “insurmountable” even more so, so I suppose “surmounted” does actually appear in a related context (as in “that difficulty has been surmounted”), but it’s still relatively unusual. I suspect that there are other words, English words as opposed to mathematical terms, that just don’t show up very often outside of the exercises in a text.

Here is a Norman Window, by the way, from Notre-Dame d’Étretat in Étretat, France.

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