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Harrierfalcon
The Raptor of Calcs
Super Elite (Last Title)
Joined: 25 Oct 2006
Posts: 2535
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 Posted: 17 Dec 2006 04:43:30 pm Post subject: |
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Sorry for getting 'off topic' but here's another brain teaser:
Try to come up with ANY program at all that will calculate the exact angle formed by the 2 hands of an analog clock, given the time.
I spent all day today noodling this, and I finally came up with one. This one is not for size, but simply doing this.
Challenge: Try to do it without using any built-in formulas. Not really a challenge (mine uses none).
Reason being, we had to do this in Geometry, and for finals we got a cheat sheet we can write anything on. My teacher says that its in case anyone happened to program it into their calculator. |
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DarkerLine
ceci n'est pas une |
Super Elite (Last Title)
Joined: 04 Nov 2003
Posts: 8328
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| Posted: 17 Dec 2006 04:55:33 pm Post subject: |
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[font="courier new;font-size:9pt;line-height:100%;color:darkblue"]Prompt H,M
abs(30H-5.5M
min(Ans,360-Ans
(returns result in degrees)
Not sure what you mean by "no built-in formulas," is this good enough?
Last edited by Guest on 17 Dec 2006 04:59:01 pm; edited 1 time in total |
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Harrierfalcon
The Raptor of Calcs
Super Elite (Last Title)
Joined: 25 Oct 2006
Posts: 2535
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| Posted: 17 Dec 2006 05:36:14 pm Post subject: |
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Goshdangit. How advanced in math are you? I'm a freshie in Honors Geometry.
As my brother would say, migglesphlit.
Would you mind explaining how that works? Just the last 2 lines--I'm pretty sure I know what the first 1 does.
Last edited by Guest on 17 Dec 2006 06:32:11 pm; edited 1 time in total |
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DarkerLine
ceci n'est pas une |
Super Elite (Last Title)
Joined: 04 Nov 2003
Posts: 8328
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| Posted: 17 Dec 2006 07:38:32 pm Post subject: |
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To find the angle between the hour hand and the minute hand, I find the angle between 12 o'clock and the hour hand, and subtract the angle between 12 o'clock and the minute hand. The difference could be negative, so I take abs() of it, and it could be something like 330 degrees, so I take the smaller of the two possible angles.
If we can assume that the hour is 0 to 12, then the angle for the hour hand is 30*hour (360 degrees / 12 hours). But wait - the hour hand moves during the hour too. In fact, for each minute that passes it moves 1/60 of the distance to the next hour, which is 1/60 of 30 degrees or .5 degrees per minute. So the angle for the hour hand is 30*hour + .5*minute.
For the minute hand, the degree measure is just 6 (360 degrees / 60 minutes in an hour) degrees per minute, so its angle is 6*minutes.
We subtract these, and get 30H+.5M-6M which simplifies to 30H-5.5M.
We could actually play around with common factors a bit and get the following code, which is one byte smaller, but that's petty. Nevertheless:
[font="courier new;font-size:9pt;line-height:100%;color:darkblue"]Prompt H,M
abs(6H-1.1M
5min(Ans,72-Ans
Last edited by Guest on 17 Dec 2006 07:38:44 pm; edited 1 time in total |
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