Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20121231 23:28:57
Clock ProblemQuestion 1: How to find the angle between the two hands of the clock at a given time? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20121231 23:45:48
Re: Clock ProblemHi Agnishom The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20130101 00:51:45
Re: Clock ProblemSorry, it had been too stupid question Last edited by Agnishom (20130101 00:53:18) 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #4 20130101 01:03:09
Re: Clock ProblemThat is correct. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #5 20130101 01:13:54
Re: Clock ProblemNow, how do I show that the hands of the clock come in right angles 22 times? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #6 20130101 01:17:33
Re: Clock ProblemThey do not. They are at right angles much more times. 46 times, I would say... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #7 20130101 01:26:57
Re: Clock ProblemThen 22 is the number of what? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #9 20130101 01:36:38
Re: Clock ProblemChanged my mind. I think it is 22. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20130101 03:13:53
Re: Clock ProblemActually, it is neither. We need to be given a time period on which we count the right angles... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #11 20130101 04:32:36
Re: Clock ProblemI think the problem is for a 12hour period. The simplest way is to count how many times the hands are at right angles in every hourly. #12 20130101 05:34:26
Re: Clock ProblemOh, here's the math. The angular velocity of the minute hand is 6° per minute and that of the hour hand 0.5° per minute. The difference in their angular velocities is therefore 5.5° per minute. Starting at twelve o'clock, the time taken for the hands to be first at right angles with each other is 90/5.5 minutes. Thereafter the minute hand has to turn through 180° to be next at right angles with the hour hand; the time taken for this is 180/5.5 minutes. If is the time in minutes at which the hands are perpendicular for the th time after twelve o'clock, we have the formula: There are 720 minutes in half a day. The largest integer for which is . Happy New Year! #13 20130101 05:53:27
Re: Clock ProblemAnd these are the times at which the hands are perpendicular (using 12hour notation): #14 20130101 16:36:47
Re: Clock ProblemGot it! Happy New Year! 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda 