Retina display math
01-25-2014, 10:00 PM (This post was last modified: 01-25-2014 10:10 PM by Joe Horn.)
Post: #1
 Joe Horn Senior Member Posts: 1,793 Joined: Dec 2013
Retina display math
In the Wikipedia article about "Retina Display", in the second paragraph of the "Technical definition" section, it has this phrase (DEGREE MODE is assumed):

"twice the Tan of π divided by 360 (equal to half a degree in radians)"

A few lines later it says:

"Two times the Tan of π divided by 360 can also be approximated with π divided by 180 (= 0.01745)."

Am I going senile, or are these statements mathematically whacked? According to all my HP calculators, in degree mode:

2*tan(pi)/360 = tan(pi)/180 = 0.000304923...
0.5 degrees = 0.008726646... radians
pi/180 = 0.01745329...

The article claims that the first two are equal, and that the first and third are approximately equal. But they're orders of magnitude apart. What's going on here?

It's not a degree mode versus radian mode thing. In radian mode, the first is zero and the other two remain unchanged.

EDIT: Oh, sorry, false alarm. They forgot to put parentheses around "pi divided by 360", and then it all works ok in radian mode, even though the article is entirely about degrees. Sheesh.

<0|ɸ|0>
-Joe-
01-25-2014, 10:31 PM
Post: #2
 Han Senior Member Posts: 1,881 Joined: Dec 2013
RE: Retina display math
$$2\tan(\pi/360)$$ since $$\pi/360$$ radians is half a degree

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01-26-2014, 04:59 AM
Post: #3
 Joe Horn Senior Member Posts: 1,793 Joined: Dec 2013
RE: Retina display math
(01-25-2014 10:31 PM)Han Wrote:  $$2\tan(\pi/360)$$ since $$\pi/360$$ radians is half a degree

That's what alerted me to the missing parentheses: their mention of "half a degree in radians". I'm so accustomed to the "order of operations" rule that at first I just blindly did exactly what they said, without thinking. Lesson learned.

<0|ɸ|0>
-Joe-
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