12-hour clock in the context of "24-hour clock"

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⭐ Core Definition: 12-hour clock

The 12-hour clock is a time convention in which the 24 hours of the day are divided into two periods: a.m. (from Latin ante meridiem, translating to "before midday") and p.m. (from Latin post meridiem, translating to "after midday"). Each period consists of 12 hours numbered: 12 (acting as 0), 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The 12-hour clock has been developed since the second millennium BC and reached its modern form in the 16th century.

The 12-hour time convention is common in several English-speaking nations and former British colonies, as well as a few other countries. In English-speaking countries: "12 p.m." usually indicates noon, while "12 a.m." means midnight, but the reverse convention has also been used (see § Confusion at noon and midnight). "Noon" and "midnight" are unambiguous.

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👉 12-hour clock in the context of 24-hour clock

The modern 24-hour clock is the convention of timekeeping in which the day runs from midnight to midnight and is divided into 24 hours. This is indicated by the hours (and minutes) passed since midnight, from 00(:00) to 23(:59), with 24(:00) as an option to indicate the end of the day. This system, as opposed to the 12-hour clock, is the most commonly used time notation in the world today, and is used by the international standard ISO 8601.

A number of countries, particularly English speaking, use the 12-hour clock, or a mixture of the 24- and 12-hour time systems. In countries where the 12-hour clock is dominant, some professions prefer to use the 24-hour clock. For example, in the practice of medicine, the 24-hour clock is generally used in documentation of care as it prevents any ambiguity as to when events occurred in a patient's medical history.

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12-hour clock in the context of Solar noon

Noon (also known as noontime or midday) is 12 o'clock in the daytime.

Solar noon is the time when the Sun appears to contact the local celestial meridian. This is when the Sun reaches its apparent highest point in the sky, at 12 noon apparent solar time and can be observed using a sundial. The local or clock time of solar noon depends on the date, longitude, and time zone, with Daylight Saving Time tending to place solar noon closer to 1:00pm.

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12-hour clock in the context of Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.

A familiar example of modular arithmetic is the hour hand on a 12-hour clock. If the hour hand points to 7 now, then 8 hours later it will point to 3. Ordinary addition would result in 7 + 8 = 15, but 15 reads as 3 on the clock face. This is because the hour hand makes one rotation every 12 hours and the hour number starts over when the hour hand passes 12. We say that 15 is congruent to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12).

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