I am a above maths abecedary and buyer of DoingMaths. I adulation autograph about maths, its applications and fun algebraic facts.

As any schoolchild can acquaint you, there are 360 degrees in a abounding circle. By agreeable a amphitheater up into 360 according slices we can afresh admeasurement any bend of about-face that we like, whether it be bisected a about-face (180°), two complete turns (720°) or any added admeasurement of angle. But why do we use 360°? Why did somebody aces this allegedly accidental cardinal and not article abroad like 10, 100 or alike 540?

There are added systems such as radians (splitting a amphitheater into 2π pieces) or alike gradians (splitting a amphitheater into 400 pieces), but it is still the 360 degrees that we tend to use in accustomed life.

While cipher is abiding of the exact origins of the use of 360, there are several hypotheses which we will accept a attending at here.

One abeyant acumen for the use of 360° is in the sexagesimal arrangement acclimated by the age-old Sumerians and Babylonians. Whereas we use the base-10 decimal arrangement of calculation which appearance ten digits 0-9, the base-60 sexagesimal arrangement uses sixty audible symbols.

Just like our decimal arrangement analogous up with bodies accepting ten fingers, the sexagesimal arrangement can additionally be affiliated to fingers and hands. Anniversary feel has three duke (the collective area two feel basic meet). Ignoring the thumb, this agency that you accept 3 × 4 = 12 duke on one hand. Whereas we may accumulate clue of numbers by counting on our fingers, with anniversary feel apery 1, we could calculation on our duke instead. By accomplishing this we could get to 12 on one hand.

Once we ability 12, we can accession one feel on the added duke to represent the actuality that we accept already counted one set of duke and afresh alpha counting afresh on the aboriginal duke . As we accession one chiffre for anniversary 12 duke that we calculation and there are bristles digits on one hand, we can get to 5 × 12 = 60 afore active out of fingers and knuckles. In this way, the sexagesimal arrangement is aloof as advantageous for animal calmly as the added accustomed decimal system.

After the Sumerians and Babylonians, the sexagesimal arrangement was afresh anesthetized on to the age-old Egyptians who, with their adulation of geometry, realised that you could fit six boxlike triangles calm into a abounding amphitheater such as in the diagram below. The Egyptians had already absitively that anniversary bend of an boxlike triangle was their favourite cardinal 60°. This afresh makes the abounding amphitheater according to 6 × 60° = 360°.

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Another abeyant antecedent of our use of 360° is in the calendars of the age-old world. It has been accepted for abounding bags of years that the Earth takes about 360 canicule to biking about the Sun. The age-old Persians for archetype had a 360 day agenda with an added intercalation ages added in to accumulate the agenda in band with the seasons (essentially analogous our accepted 365 day calendar). If you accept a 360 day calendar, afresh it is a analytic footfall to accept that the Earth campaign 1/360 of its apogee per day, appropriately agreeable the annular apogee into 360 according pieces.

Furthermore, if we booty the boilerplate of the about 365 day solar year and the about 355 day lunar year, we afresh get 360 days.

The third acumen for application 360 is that although on aboriginal glance it may assume like a accidental cardinal and harder to use than a ability of ten such as 10 or 100, it has one decidedly advantageous property; its ample cardinal of factors (numbers that bisect into addition cardinal altogether after abrogation a remainder).

Having a ample cardinal of factors agency that 360 can be disconnected up acutely easily. If we appetite to breach the amphitheater into two, we can do 360º ÷ 2 = 180º, a accomplished number. If we capital to breach the amphitheater into twelve genitalia we can do 360º ÷ 12 = 30º, addition accomplished number.

In actuality 360 has 24 factors; 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360 itself. We could breach a amphitheater appropriately into any of these numbers after accepting to use decimals, fractions or actual bits. If we analyze this to added numbers such as 10 with its four factors and 100 with nine factors we can see aloof how accessible it is to bisect 360º into according slices in altered ways.

360 is accepted as a awful blended number. This agency it has added factors than any cardinal beneath it. If we capital a cardinal with alike added factors, we would accept to go all the way up to 720 which has 30 factors.

As we accept already seen, there is added to the best of 360 than aloof its factors, but this affluence of analysis makes 360 an ideal cardinal of degrees behindhand of how this cardinal was originally conceived.

This agreeable is authentic and accurate to the best of the author’s ability and is not meant to acting for academic and abundant admonition from a able professional.

© 2021 David

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