Lambdia
Explorer
Le Playbook

Angle

2 articles
AlidadeAngle of arrivalAngle of incidenceAngle of listAngle of viewAngular apertureAngular diameterAngular displacementAngular frequencyAngular meanAngular micrometerAngular resolutionAngular wavenumberAnti rolling gyroApproach and departure anglesArcfourthArchipendulumArcminuteArcsecondArcthirdArgument of periapsisAstrolabeAxis angle representationAzimuth+ 109 de plus
GeometryLycéeExplication9 min

Sixteen and Four Elevenths Minutes Past Three

The long hand turns 6 degrees a minute and the short one half a degree, so a 90 degree gap closes at 5.5 degrees a minute and the hands coincide 180/11 minutes past three, at 3:16:21.8181. At 3:15 the long hand has reached the 3 and the short hand is 7.5 degrees ahead of it, which is the whole content of the wrong answer. Consecutive coincidences are 720/11 minutes apart, so there are eleven per twelve hours and twenty-two per day, and the common phrasing "eleven times a day" is wrong by a factor of two.

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GeometryCollègeExplication8 min

Seven and a Half Degrees at a Quarter Past Three

At 3:15 the minute hand is on the 3 and the angle between the hands looks like zero. It is 7.5 degrees, or pi/24 radians, because the hour hand crawls a quarter of the way from the 3 to the 4 while the minute hand travels a full lap. The zero answer is exact for a clock whose hour hand waits on each numeral and jumps, which is not a clock that exists.

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