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Clock problem mathematics
When the minute hand is in front of the hour hand, the angle formula is n * 6-(m * 30+n * 0.5), and when the minute hand is behind the hour hand, the angle formula is (m * 30+n * 0.5)-n * 6. Where n is minutes and m is hours. Degree is a number measured in degrees and refers to the standard used for measurement. Clock is a precise instrument for measuring and displaying time. Mathematically, the minimum positive angle formed by the intersection of two straight lines is called the included angle of these two straight lines (or vectors). Related information: The common examination form of clock problem is clock face drawing. The problem of clock traceability is usually to study the position between the hour hand and the minute hand, such as "coincidence, verticality, alignment and angle between the minute hand and the hour hand" The hour hand and the minute hand move in the same direction, but at different speeds, which is similar to the catch-up problem in travel problems. The key to solve this kind of problem is to determine the speed or speed difference between the hour hand and the minute hand. In the concrete problem solving process, we can use the grid method, that is, divide the circumference of the clock face into 60 grids on average, and each grid is called 1 grid. The minute hand walks every hour, that is, 60 minutes, while the hour hand only walks 5 minutes, so the minute hand walks 1 minute and the hour hand walks112 minute. The speed difference is1112. You can also use the degree method, that is, from the angle, the circumference of the clock face is 360, the minute hand rotates 360/60 degrees per minute, that is, the minute hand speed is 6/ minute, and the hour hand rotates 360/ 12=30 degrees per hour, so the minute speed is 30/60, that is, 0.5/ minute. The speed difference between the minute hand and the hour hand is 5.5/ min.