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    It is in a way the most civilized of all the cardinalsand its use is only forced on us by the needs of cultivated modes of thought. Mesopotamian science Knowing this can save the life of you and yours. He says that a battler has variously been referred to as a bird, a swagman or a prostitute. Above all, have fun. As a number, zero means nothing —an absence of other values.

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    In this science game you need to face three tests to find well-guarded treasure in an ancient temple. There are over prizes on offer for K students, in the categories of Working Scientifically, Working Technologically and Working Mathematically, so every student has the opportunity to win a prize. Although zero became an integral part of Maya numerals, it of course did not influence Old World numeral systems. Nerves that made your mouth water when you smell good food get mistakenly connected to the tear gland instead.

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    Why has geometry not been 'metricked'? Why degrees intstead of 1, 10, or even ? David Hughes, Toronto, Canada Because one of the essential varibales in geometry is the number three. For example, three being a factor of means that an equilateral triangle has angles of 60 degrees.


    What would their angles be in a metric system? It originated in France as the 'grade' along with other metric units. I only know of the French artillery actually using it. Angular measurement in degrees or radians is given in reference to a circle, degrees or 2 Pi radians being the measure one full revolution.

    If we were to divide a circle into anything other than deg we would have to change our calendars too - the ancient Greeks worked out that there were days in the year, and that, therefore, we progress about the sun at one degree per day - they were quite close given that they worked on observation alone! Peter Clark, Cambridge, UK The degree is an arbitrary unit; basically any division of a circle would work as a system of measurement. There is a more fundamental unit call the Radian.

    This is the angle subtended by an arc of a circle equal in length to its radius. Since the circumference of a circle is 2 x pi x radius one there are 2 pi, or 6. This is fine for calculations on angular motion but difficult to work out in your head. Ray Gallagher, Belfast, Northern Ireland We inherited degrees from the Babylonians, but many ancient societies were highly interested in astronomy and in some megalithic Britain?

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    This is logical, since the earth turns on its axis times a year. Their measurements seem to have been interrelated and not arbitrary as a metrically divided circle would be. The Babylonians probably reduced this to as it divides so much more easily by many factors. After some time struggling to get it to work, I noticed that the scale on which horizontal angles were measured read degrees rather than My supervisor told me that this was and old piece of equipment, once part of an attempt to metricise the circle.

    I'm not sure whether this was purely an Italian initiative or not! That number turns out to be the smallest one whose quotient is an integer when divided by any whole number from 1 through 10 except for 7, which may have added to seven's stature as a "magic number". I've heard that at least in the U. Although they did have a figure for 10 so their number 11 was still written as figure of 10 next to figure of 1.

    The origin of this is not known for sure although they were obviously influenced by astronomy and the fact that there are almost days in a year. They also came up with sixty minutes in the hour, 24 hours a day. This is only another example of the slipping of school standards that we only expect school children to only know 9 figures and zero Kamyar, Samos Greece Because you usually want to know how far round the circle you are, and you can divide into many more useful fractions.

    Indeed, the unit favoured by mathematicians isn't the degree but the radian. So rather than 90 degrees you say 'pi-over-two radians. There are grads in a right angle, or grads in degrees It is still in use by the French military and pocket calculators have degree, radian, and gradian modes for trigonometric functions.

    There are grads to the right angle, to the full circle. The calculator accessory that comes with the Windows operating system allows you to select working in grads rather than degrees or radians. Nick Rouse, Plumpton Green UK Whilst mathematicians are happy with degrees, or more usually radians as the maths gets more advanced, others have indeed split angles into The gradian or grad is the unit of measurement which is obtained by splitting a right angle 90 degrees into parts.

    The military have a fondness for this form of angle measurement and it is easy to obtain a compass set up this way. I imagine there are others in use - after all the degrees is purely arbitrary and a historical left over from the Babylonian sexagesimal counting system, rather than a deliberate choice. Hayden Rissbrook, Walthamstow, UK Whilst mathematicians are happy with degrees, or more usually gradians, as the maths gets more advanced, others have indeed split angles into I imagine there are others in use, afterall the degrees is purely arbitrary and a historical left over from the Babylonian sexagesimal counting system, rather than a deliberate choice.

    Hayden Rissbrook, Walthamstow, UK has many more divisors than 10,etc. Therefore a circle can be divided more easily into many diferent equal parts - 2,3,4,5,6,8,9, Try doing that with or Lewis, London, UK The use of gon instead of degrees can also be found in land surveying as well. Some theodolites will have the option of degrees or gon and many that were made in the former eastern block used this system.
    These are the nodes of the moon and their usage in astronomy is important for predicting the eclipses of the Sun and the Moon.

    Although they possess no mass or density, they are treated as planets in the sense that they have an effect on human affairs. Nakshatras Whatever constellation nakshatra the Moon was in at sunrise, the entire day was named after it.

    The nine rulers of the nakshatras are repeated three times in sequence. So in this sense you can say that the Hindus followed a nine-day week. The same effect as a weekday is thereby achieved in terms of socio-religious significance. Whereas the Chaldeans used an unbroken consecutive day count of hour and day rulers, the Hindus used a more concrete system of the observable Moon in a group of stars. But there is a common thread that is stitched between both the seven-day week and the twenty seven nakshatras.

    Putting the stars Gods of the 7 day week on a circle with Sunday at the top, we get: Now in Figure 4, we may make room for two more planets: Whatever the case may be, if we were to add two more planets to this seal the obvious place would be in the areas vacated by the points of Jupiter and Mercury.

    Their placement in the seal is shown in Figure 5. Hindu Astrology treats the nodes as planets even though they possess no mass and density. They are sensitive points where the path of the Moon crosses the path of the Sun.

    Being invisible, it is quite fitting that they should not have a point of the star aiming at them in the diagram shown above. But note the general position of the planets and see how they are unchanged from the Chaldean star order.

    The next diagram, Figure 6, will show the connection with the Hindu nakshatra order. Compare this diagram with Table 2, Nakshatras and Rulers. Here the order is clockwise starting with Ketu, going to Venus, the Sun, down to the Moon, back up to Mars, over to Rahu, Jupiter, Saturn and finally bypassing over to Mercury.

    In fact, this diagram may taken as a single pointed star with the significant planet being at the single point. It seems that the similarities between Hindu astronomy and Chaldean magical seals are too great to be a mere coincidence. It is quite likely that the two share a similar origin or that one was derived from the other. But since ancient Hindu tradition and current usage make more consistent usage of a direct base sixty system of counting, and the other cultures use a derivative of that, it seems more likely that the sexagesimal is of Hindu origin.

    It may be argued that the sexagesimal was not founded upon the joint cycles of Jupiter and Saturn but upon some other measurement such as the average number of three hundred and sixty days in a year. This, of course, is assuming that ancient man was incapable of counting the correct number of days in a year and that he was infinitely unclever. For the sake of argument, let us accept that position. There still remains the problem of dividing the year into parts that would yield a base sixty system of counting.

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    The Babylonians divided their year into three seasons. The Hindus, however, divided their year into six seasons. Of the two cultures which would arrive at a base sixty system? But judging from the rest of Hindu astronomical techniques it is clear that they knew precisely how long was the solar year.

    All the other planetary cycles were also studied with great scrutiny. From this it may be tempting to think that the sexagesimal was arrived at in order to provide the great average mean of measurement for celestial phenomena just as today the binary mode of counting is most convenient for computer science. Three hundred and sixty, which is a multiple of the sexagesimal, is the midpoint number between the day solar year and the day lunar year.

    One synodic period of Mars is days which is equally divided by 60 thirteen times. Between two consecutive conjunctions of Saturn and Jupiter in a twenty year period, Mercury will go retrograde a little over sixty times. The Hindus also based their knowledge of breath control, Pranayama, upon the sexagesimal system. In one twenty four hour period, or between two consecutive sunrises, a person takes an average of breaths, each breath being four seconds long.

    This number, divided by 60 equals Cosmological Cycles The structure of Hindu astronomy is built upon the foundation of an unique concept of cosmological time cycles.

    No other culture on Earth has or is known to have such a unique system of Cosmology. The only other culture to come close to the vast scale of time conceived by the Hindus are the Mayan. The astronomical quantities derived from these cosmological time cycles are vastly more accurate than anything achieved by the Greeks. And they were in use at a time when the Britons were still living a neolithic lifestyle. Outline of Time Scales Prior to the creation of the universe, Lord Vishnu lies asleep on the ocean of all causes.

    He rests upon a serpent bed with thousands of cobra-like hoods. While asleep, a lotus sprouts from His navel. Upon this lotus is born Brahma the creator of the universe.

    Lord Brahma lives for a hundred years and then dies, while Lord Vishnu remains. One year of Brahma consists of three hundred and sixty days. At the beginning of each day Brahma creates the living beings that reside in the universe and at the end of each day the living beings are absorbed into Brahma while he sleeps on the lotus. One day of Brahma is known as a Kalpa. Within each kalpa there are fourteen manus and within each manu are seventy one chatur-yugas. Each chatur- Yuga is divided into four parts called yugapadas.

    From the first chapter of Surya-Siddhanta, the most revered authoritative source of Hindu astronomy, we have the following passage: That which begins with respirations prana is called real. Six respirations make a vinadi, sixty of these a nadi: And sixty nadis make a sidereal day and night. Of thirty of these sidereal days is composed a month; a civil savana month consists of as many sunrises; A lunar month, of as many lunar days tithi ; a solar Saura month is determined by the entrance of the Sun into a sign of the zodiac; twelve months make a year.

    This is called a day of the gods. The day and night of the gods and of the demons are mutually opposed to one another. Six times sixty of them are a year of the gods, and likewise to the demons.

    Twelve thousand of these divine years are denominated a chatur- Yuga ; of tena thousand times four hundred and thirty two solar years is composed that chatur yuga, with its dawn and twilight. The tenth part of a chatur-yuga, multiplied successively by four, three, two, and one, gives the length of the krita and the other yugas: One and seventy chatur-yugas make a manu; at its end is a twilight which has the number of years of a krita-yuga, and which is a deluge. In a kalpa are reckoned fourteen manus with their respective twilights; at the commencement of the kalpa is a fifteenth dawn, having the length of a krita yuga.

    The kalpa, thus composed of a thousand chatur-yugas, and which brings about the destruction of all that exists, is a day of Brahma; his night is of the same length.

    His extreme age is a hundred, according to this valuation of a day and a night. The half of his life is past; of the remainder, this is the firsts kalpa. And of this kalpa, six manus are past, with their respective twilights; and of the Manu son of Vivasvat, twenty seven chatur yugas are past; Of the present, the twenty eighth chatur yuga, this krita yuga is past.

    Now to make plain what is stated above. A night of the gods is half a sidereal year. Each of these days being two kalpas long. Verse 23 shows that the Surya-Siddhanta was composed right after krita-yuga and during the treta-yuga. The present yuga we are in right now is the kali-yuga which is said to have begun on Friday February 18th BC of the Julian calendar. This becomes clearer when represented in a tabular form.

    Infrastructure of the Chatur-Yuga period Divine Years.

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