Archive for August, 2016

Calculating Fahrenheit

August 15, 2016

Thermometer_Hotel_BaronThe 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.

Another Math Mistake:

August 13, 2016

640px-OmnogoviLandscape (1)

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!