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Magic Number.


nootelepat

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Magic number.

 

Another mystery of our existence.

The vast majority of people living on Earth now six and a half billion fellows do not even think: why in the hour -60 minutes (rather than say, 100), and in a minute-60 seconds? Why are signs of the zodiac and the months of the year 12 (not 10, that it would be convenient). "We are lazy and not interesting" - (Pushkin). But still, even the most stupid, lazy and incurious people of today, I'll try to explain something of the secret knowledge. Although it is usually hidden from the profane!

In the infinite number of numbers is an amazing case where the sum of squares of five neighboring numbers equal to each other: 10 (squared) +11 (squared) +12 (squared) = 13 (squared) +14 (squared). Everyone can produce a simple mathematical operations, and to see for yourself: in the first and second half of this equation is obtained 365.I just that magic number -365 days-now expressed in the mean time of one full revolution of the Earth in its orbit around the Sun. That is, the earth's year. Such mathematical and astronomical OVERLAP seems almost incredible, unless you assume the intervention of foreign forces REASONABLE.

I repeat, especially for blunt (ie, for people with upper education): 10, 11, 12, 13, 14, a consecutive number one after the other, not selected specifically for the establishment of equality. And there in the mathematics of another series of successive numbers, simple mathematical manipulations that would provide similar amazing results!

For example, if you simply add the number of this series (10 +11 +12 +13 +14), we get 60 the number of seconds in a minute, the number of minutes in an hour. Well, the arithmetic mean of these five wonderful numbers will be 12 the number of all perfect.

However, such mathematical calculations are involved in the Babylonian priests, finding in this great wisdom. They found signs of the zodiac, and 12, and 12 months of the year, and the concept of "lucky dozen," and consisted of five 12-year cycles over 60-year cycle in the eastern calendar.

As you can see, all these shape our lives and the number of units of time-linked in one system. That is some incredible mathematical, chronological and astronomical coincidence!

I wonder: who is over nesmyshlenymi us, making fun of? Who are all these coincidences trick? Who through the impenetrable stupidity of humanity, yet there are such unequivocal signs TRUE world order?

Well do not the priests of the same Babylonian Winged orbit and the speed of the Earth's rotation around its axis under a rare mathematical equality of consecutive numbers!

 

Sergei Tsimbalyuk

Independent researcher

www.nootelepat.narod.ru

 

PSMozhno say more, but there is a danger of overheating brains profane redundant information! Incidentally, the average distance between Earth and the Moon (384 000km) is practically equal to 60 average radius of the Earth (6370km). On what market is all of course just a coincidence!

 

GREAT MYSTERY OF THE MOON AND THE EARTH.

 

In addition, my article "magic number" Christopher Knight and Alan Butler in his remarkable book "The Mystery of the Moon" offers the following coincidence.

1) The diameter of the Sun is 109.2 Zemli.A diameters in distance from the Sun to the Earth fits 109,2 diameters of the Sun! Of course, that the circle of the sun equals 109.2 Earth's circumference. 0.5 Earth's diameter (its radius) is the basis for determining the distance to the sun and planets, as well as their size in kilometers.

2) Equatorial circumference of the moon, strangely enough, 10 920 km, ie 100 km multiplied by 109.2.

3) Circle of the Moon at exactly 400 times smaller than the circumference Solntsa.V time a total solar eclipse of the distance from Earth to the Sun in exactly 400 times greater than the distance from Earth to the Moon at a given point of its elliptical orbit! Eccentricity of the Earth and Moon can, for example, and this ratio: 152 000 000km: 380 000km = 400.I This is obtained by dividing the two radii of the orbits of the number 400 is being built into a cube - in determining the mass of the Sun by a formula refined Kepler's third law!

4) Moon rotates around its axis at a speed of exactly 400 miles in one terrestrial day.

Velocity of rotation of the Earth at exactly 100 times greater.

5) If you multiply the circumference of the moon in kilometers of the Earth's circumference and divide by 100 turns the circle of the sun!

6) Circle of the Moon is 27.3 per cent of the circumference of the earth.

7) Moon makes one revolution in its orbit around the earth every 27.3 Earth days! If 27.3 is multiplied by 4 is obtained already familiar number 109.2. Complete revolution around its axis Moon also commits to 27.3 Earth days.

8) 100:366 = 0,273. Last year, Earth makes 366 revolutions around its axis relative to the stars (if extremely accurate speed 366.259). And the circumference of the Earth is 366 percent of the circumference of the moon! (If extreme accuracy 366.175 per cent).

Period of the Earth around the sun 366 days and the period of the Moon around the Earth 27.3 days also determine the mass of the Sun by the formula of an improved third Kepler law.

Different parts of the latitude of the Sun rotate at different speeds: a complete turnover from 25 days at the equator to 30 days near the poles. You can laugh - but the average is obtained approximately 27.3 Earth days!

9) The apparent angular diameter of the sun and the moon is the same and equal to 0,5 gradusa.Poetomu coincidence of the lunar disk with a solar eclipse in full-as seen from Earth is absolutely polnym.I this fact must be acknowledged as the greatest miracle since its probability is negligible mala.Ni one other planet does not have anything like that, there just does not happen total solar eclipses! Solar eclipses occur two to five times a year, but the area of a total eclipse is very small - so anywhere in the earth's surface complete eclipse happens only once in 360 years! Number-then what a special and famous!

So, before you a series of "coincidences" which are formed in a regular now - an inexplicable within the framework of the theory of probability.

 

Only complete tupari may declare that all of the above-coincidence.

If someone refuses to consider the explicit laws, because it believes that they should not be - he does not see anything except their own prejudices! These little people are the only obstacles in the path of knowledge.

 

Sergei Tsimbalyuk

Independent researcher

www.nootelepat.narod.ru

R.S. The ancient Greeks there was a strange tradition that in the distant past the Moon in the sky was not.

This so-called antediluvian times.

Even tupari might think: what monstrous earthquakes and floods could cause an unexpected appearance in the immediate vicinity of the Earth such a huge manmade object, like the Moon!

 

P.P.S. For particularly hard-nosed, I have to lay out the statistics NASA - which are based on Knight and Butler in their calculations.

The equatorial diameter of the sun 1 392 000km.

AVERAGE diameter of the Earth on 12 742km (756km equatorial 12).

So along the diameter of the sun in the middle can be placed 109.245 Earth disc.

The amount of the diameters of the Sun within Earth's orbit 109.267 (when the Earth is at the aphelion of its orbit - to the maximum distance from the sun).

Average circumference of the Sun 4 373 096km.

The average distance from the Sun to the Earth (astronomical unit) 149.6 million km (but the distance at the aphelion of the orbit 152,1 million km!).

Polar circle the Earth 39 941km on the assessment of NASA, other sources give 40 008km (054km equatorial 40).

Equatorial circumference of the moon 10 920.8 km (average circumference of 10 914.5 km).

The average distance from Earth to the Moon 384 500km. (Perigee, 363 000km, apogee 405 000km).

Moon moves in its orbit around the Earth at an average speed of 1 km in sekundu.Eta rate changes experienced by 0,964 kilometers per second to 1,076 kilometers per second.

The exact period of the Moon around its axis and around the Earth 27.322 Earth days.

Finally, there are arbitrary units "meter" and "second": on Earth pendulum with a length of 1 meter - will swing at a speed of 1 times per second! Due to the gravity force (gravity) MASS Zemli.Eto understood by the ancient Sumerians (the teachers of the Babylonian priests), who had a measure of length - ideentichnaya meter! But modern tuparyam it does not understand ...

 

 

EDUCATING FOR DARK MIND.

You seemed just an amusing fact that the diameter of the sun falls 109,2 diameter of the Earth-and in distance from Sun to the Earth fits exactly 109,2 diameters of the Sun?

However, this distance is called the Astronomical Unit, and this determines the value of the majority of astronomical calculations! Only the knowledge of the value of the distance from the Sun to the Earth and the distance from the Earth to the Moon possible to determine the mass of the Sun and the mass of the planets of the solar system!

Well, that's the formula, the proportion also only funny?

Distance from the Sun to any planet relates to distance from the Sun to the Earth as well = as the square of the velocity of the Earth's orbit around the Sun relates to the square of the velocity of the above any planet in its orbit around the Sun. (There is a clear analogy and connection with the formula of equality of the mass ratios and accelerations of two interacting tel.Mezhdu other things, identify this equation pseudoscientific boobies were only able to by numerous experiments!).

Simply put, the speed of any planet in the solar system is inversely proportional to the distance of the planet from the Sun, and this proportion is absolutely rigid.

Even simpler: if, for example, divide the square of the velocity of the Earth to the square of the velocity of Mars, the result obtained distance from the Sun to Mars, as defined in astronomical units!

The speed of the planets themselves is determined by this formula in kilometers per second.

If you are not lazy, you can calculate yourself and check! Or microcalculator lost-and without it already and have forgotten how to take it?

Summary 1: It turns out that the distance from sun to the earth, and the velocity of the Earth in its orbit and are proportional to the number of multiples of 109.2.

If the velocity of the Earth 29.8 km / sec divided by stellar orbital period of the moon 27.3 days, we get 1,092.

Summary 2: indirectly (through refined Newton's third law Kepler's formula) is the number 109.2 should pass through the value of the masses and orbits of axes of all the planets!

Simply put: the mass and the axis of the orbit of a planet must be multiples of the magic number of 109.2. (Of course, that magic number of 27.3, too!). But the Sun's mass is a multiple of it just by definition!

Summary 3: The stupidity of the herd of two-legged watching us!

Summary 4: Normally, I write my articles per readers poludebilov (that is as simple and convincing). But this time the theme allows only the sophisticated system of evidence.

 

The final conclusion:

All of the above PROVES that the formation of masses of the planets and their distribution in orbits around the Sun's mass-place on a certain strict laws of quantum gravitoniki (by analogy with quantum mechanics!).

That is: the material of the primary gas-dust clouds were differentiated (according to their density per unit volume) the gravity of the sun in accordance with some waves (or zones), probability and more precisely in the middle (at maximum) of these waves was gradually concentrated in the form planets.

CONCLUSION grandiose:

Thus, it turns out that the law of quantum gravitoniki severely prejudice the inevitable formation of terrestrial planets: a certain weight, at a certain distance, at a certain speed dvizheniya.To is obtained that the emergence of so favorable for the existence of protein life on the planet like the Earth, was initially predetermined by strict the laws of physics!

It turns out that the emergence of (near a Sun-like stars), planets with favorable for the existence of living conditions of the protein is simply a necessary consequence of the physical laws of our universe!

But such stars-average performance, as we know, the majority.

 

Sergei Tsimbalyuk

Independent researcher

www.nootelepat.narod.ru

PSDopolnenie for those - who microcalculator hopelessly lost (but with brains - napryazhenka!).

Velocity of motion of the Earth in its orbit at 29.78 kilometers per second.

Velocity of motion of Jupiter 13km per second.

Square of the velocity of the Earth divide by the square of the velocity of Jupiter

(29,78 x29, 78): (13x13) = 5.46.

Distance from the Sun to Jupiter (on the book) is equal to 5,203 astronomical edinits.Kak see - the error is minimal! Less than one percent. (Just EXACT speed of Jupiter, I suppose, a little more than 13km).

And for this same formula can calculate the distance from the Sun to any planety.Gravitatsionnaya strength of the mass of the sun determines the speed at which the planet (and each atom separately!) Flies in an orbit at a given distance from the Sun.

This formula-ratio seems to be simple - but in any book on astronomy, I have not seen it. I had to strain - and bring yourself! It is certainly very similar to the formula of equality of treatment of the masses and accelerations of two interacting tel.Uzh in any case, my formula is much more serious and more accurate formula Titius-Bode! A no brainer this primitive rule - a horde of stupid science-like-ostepenennyh withdraw failed!

Another calculation:

Jupiter makes a complete revolution in its orbit of the Earth 11,86 years.

Distance from the Sun to Jupiter 5,203 astronomical units.

The first number is squaring, and the second in a cube.

11,86 x11, 86 = 5,2 x5, 2x5, 2.

You can, of course, to say: yes it's Kepler's third law ...

But my-formula EASIER!

Most important: According to this formula, even the Babylonian priests could easily calculate the distance to the planets (by comparing them with the distance from the Sun to Earth) - for the period of revolution of the planet in its orbit can be established by simple astronomical observations.

P.P.S. Laughter for the sake of tuparyami: average speed of the Earth in its orbit 29,78 km - about 10 000 times smaller than the speed of light in vacuum (the Moon slows down the flight of the Earth - otherwise it would be quite accurate!).

And for 10 000 days Moon makes 366 revolutions around the Earth

366x27, 3 = 10 000. (Further see paragraph 8 of "the great mystery of the moon and the Earth!)

8) 100:366 = 0.273. Last year, Earth makes 366 revolutions around its axis relative to ZVEZD.A circumference of the Earth is 366 percent of the circumference of the moon!

When I write:

"And that's what obtained by dividing the two radii of the orbits of the number 400 cube - when determining the mass of the Sun by the formula of an improved third Kepler law!

Period of the Earth around the sun 366 days and the period of the Moon around the Earth 27.3 days also determine the mass of the Sun by the formula of an improved third Kepler law. "

- a wise man could figure out - on the contrary, it determines the mass of the sun all these numbers!

I, Sage, said:

At the same distance from the Sun, the celestial bodies with different masses - must be pulled by the gravity of the Sun with different force. Thus, the sun attracts the earth is much stronger - than the Moon!

Consequently, if the Moon was once an independent planet - the radius of its orbit was larger than the radius of the orbit of the Earth! But, because of the eccentricities of their orbits, sooner or later had to cross. Since all the planets revolve around the Sun in one direction - the speed of the moon was only a few kilometers per second LESS zemnoy.I Earth, flying by, its force of gravity - has the moon in tow!

This fateful meeting occurred when the Earth's aphelion velocity was minimal - and the Moon at perihelion MAKSIMALNA.I at this decisive moment - the force of gravity of the Sun and the Earth, acting on the moon, ADD!

Developing the idea of the capture of the moon's gravity of Earth.

Most neobyazyatelno assume that this happened simultaneously. Over 4 billion years - of such meetings, confrontation of the Earth and Moon were numerous. And with every heave of gravity flying past the Earth - the orbit of the moon move up closer and closer to the Earth's orbit. Sooner or later - Moon was bound to become a satellite of the Earth!

Strictly speaking, it is logical to assume - that the other planets have collected their satellites in the same way!

REPEAT:

Different parts of the latitude of the Sun rotate at different speeds: a complete turnover from 25 days at the equator to 30 days near the poles. You can laugh - but the average is obtained approximately 27.3 Earth days!

In the polar region of the solar rotation speed of its surface, of course, is close to zero. And the average speed of 1,854 kilometers per second and average period of revolution around its axis and 27.3 days determine the angular momentum of the Sun. And he, in turn, determines the angular momentum distributed in space circumsolar Combined mass of all the planets. And, of course, the angular momentum of each of the planets separately! This is where the origin of all these in this article (and not understandable to oslonomov!) Amazing coincidences and patterns. The system of the sun and planets really can be compared with the complex and accurately balanced ticking!

Interplanetary magnetic field of the solar system has the form of large spirals, divided by the radial sector. In the neighboring sectors of the direction of the magnetic field opposite. All the spiral rotates with the sun and its rotation period is 27.3 days! (All recorded instruments unmanned spacecraft during interplanetary flights)

It seems to be easy to figure out that the gravitational field of the Sun and spiral (as with any other celestial body!) And the period of its rotation exactly the same - 27, 3 days.

In accordance with Einstein's theory: the gravitational force twists the surrounding space in the "snail".

But cattle are not pseudo-scientific ability to use logic to figure: this occurs only near the huge mass and only a short distance from the masses.

 

EXPLAIN:

According to the laws of celestial mechanics (and due to centrifugal force) the speed of rotation of the Sun around its axis - dependent distances of the planets from the sun and, of course, the speed of their movement in their orbits. Yes, and the planet's rotation around its axis - also slowed down the tidal action of gravity Sun.

Due to the action of the law of conservation of angular momentum: any spin down of the sun around its axis - is the appropriate separation of the Earth (and other planets) from the Sun! The law of conservation of momentum holds for all systems - from space bodies to the atoms and elementary chastits.Etot fundamental law of nature acting over billions of years ago - and the atoms and dust grains of the primary gas-dust clouds.

And finally the most important:

If 27,3 to square - then 745.Elementarno, Watson:

27,3 h27, 3 = 745

And at exactly 745 times the mass of the Sun large net mass of all the planets of the solar system!

The speed of rotation of the Sun around its axis 1,854 kilometers per second (1 statute mile!).

The speed of rotation of the Earth around its axis of 0.463 km per second.

Quite by accident - the speed of rotation of the Earth at exactly 4 times less than the speed of rotation of the Sun.

Covershenno accidentally moon rotates around its axis at exactly 100 times slower than the Earth.

Exactly four multiplied by exactly 100 turns 400.

Quite accidentally, the circle of the moon at exactly 400 times smaller than the circumference of the sun.

It goes: quite by accident and the Sun and Moon covershayut one revolution around its axis for 27.3 days.

 

P.S. Can the decimal number system - regarded as random chosen and whether it can be easily replaced by another? "

That thought may come to head off ONLY retarded current moronity TIME!

After all, the entire estimated geometry of our world - is based on the number Pi.

And this number (remember the same retard) - square root of 10.

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Magic number.

 

Another mystery of our existence.

The vast majority of people living on Earth now six and a half billion fellows do not even think: why in the hour -60 minutes (rather than say, 100), and in a minute-60 seconds? Why are signs of the zodiac and the months of the year 12 (not 10, that it would be convenient). "We are lazy and not interesting" - (Pushkin). But still, even the most stupid, lazy and incurious people of today, I'll try to explain something of the secret knowledge. Although it is usually hidden from the profane!

In the infinite number of numbers is an amazing case where the sum of squares of five neighboring numbers equal to each other: 10 (squared) +11 (squared) +12 (squared) = 13 (squared) +14 (squared). Everyone can produce a simple mathematical operations, and to see for yourself: in the first and second half of this equation is obtained 365.I just that magic number -365 days-now expressed in the mean time of one full revolution of the Earth in its orbit around the Sun. That is, the earth's year. Such mathematical and astronomical OVERLAP seems almost incredible, unless you assume the intervention of foreign forces REASONABLE.

I repeat, especially for blunt (ie, for people with upper education): 10, 11, 12, 13, 14, a consecutive number one after the other, not selected specifically for the establishment of equality. And there in the mathematics of another series of successive numbers, simple mathematical manipulations that would provide similar amazing results!

For example, if you simply add the number of this series (10 +11 +12 +13 +14), we get 60 the number of seconds in a minute, the number of minutes in an hour. Well, the arithmetic mean of these five wonderful numbers will be 12 the number of all perfect.

However, such mathematical calculations are involved in the Babylonian priests, finding in this great wisdom. They found signs of the zodiac, and 12, and 12 months of the year, and the concept of "lucky dozen," and consisted of five 12-year cycles over 60-year cycle in the eastern calendar.

As you can see, all these shape our lives and the number of units of time-linked in one system. That is some incredible mathematical, chronological and astronomical coincidence!

I wonder: who is over nesmyshlenymi us, making fun of? Who are all these coincidences trick? Who through the impenetrable stupidity of humanity, yet there are such unequivocal signs TRUE world order?

Well do not the priests of the same Babylonian Winged orbit and the speed of the Earth's rotation around its axis under a rare mathematical equality of consecutive numbers!

 

Sergei Tsimbalyuk

Independent researcher

www.nootelepat.narod.ru

 

PSMozhno say more, but there is a danger of overheating brains profane redundant information! Incidentally, the average distance between Earth and the Moon (384 000km) is practically equal to 60 average radius of the Earth (6370km). On what market is all of course just a coincidence!

 

This is as far as I could go before becoming astonished that you have failed to include the more fundamental sequence of squares, three squared plus four squared equals five squared. The sum of three, four, and five is twelve, which is the reason there are twelve zodiac signs and twelve months. So then, the real question becomes, do carpenters have to adjust their squares every year, since the length of the day is slowly increasing? Thank goodness we live now, and not 620 million years ago when the day was 22 hours long and the year 13 months long. Cavemen must have had a terrible time building homes with their squares so far our of whack, which is the reason they lived in caves. Also fortunately, the sun will have turned red giant long before (or perhaps because?) the day length equals the month length.

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The vast majority of people living on Earth now six and a half billion fellows do not even think: why in the hour -60 minutes (rather than say, 100), and in a minute-60 seconds? Why are signs of the zodiac and the months of the year 12 (not 10, that it would be convenient). "We are lazy and not interesting" - (Pushkin). But still, even the most stupid, lazy and incurious people of today, I'll try to explain something of the secret knowledge. Although it is usually hidden from the profane!

Fortunately, not all people are lazy and uninteresting – or uninterested. In particular, among people who commit the time and effort to participating in forums like hypography, I suspect nearly if not everyone of us have questioned how we came to have our conventional units of time, (most at an early age), and found the most plausible answers not from esoteric and occult sources (though such sources can be interesting, anthropologically :)), but from astronomy, history, a little bit of biology, and simple reasoning.

 

Why there are 12 months in a year is almost certainly because there are about [imath]12 \,\frac13[/imath] lunar cycles in a year. For prehistoric humans, most of whom presumably had difficulty counting as high as 365, but not to 12, were able to anticipate the coming seasons by counting full moons. Nearly all early (ca: 3000 BC) calendars, had twelve months, as our common modern calendars continue to, although long ago months ceased to exactly follow the Moon’s phase, but rather follow the solar year of about 365.2425 days (adding a leap day to February every year divisible by 4 but not by 100 unless also divisible by 400)

 

Though the tradition appears so early in history that its precise origins are murky, dividing the year into 12 months appears to have been extended to dividing the night into 12 hours, allowing prehistoric and early historic people to anticipate the dawn, know when to change night watch shifts, and other useful things. Ancient people appear to have estimated the hour of the night by memorizing key stars and constellations, and observing their positions. It’s fortuitous that the ration of the Moon and Earth’s periods is close to 12, as 12 is divisible by 3 and 4, the most common number of watches in a night in most cultures. The tradition of dividing the night into 12 hours appears to have been extended to dividing the day into 12 hours.

 

The dividing of hours into minutes and wasn’t popular or widely practices until practical clocks became widely available. When this happened, the idea of dividing the day and night into exactly 12 hours became less popular, because most of the time, 1/12th of a day is significantly longer or shorter than 1/12th of the night. Nonetheless, primarily for religious reasons, even after clocks allowed the even division of a full day into 24 hours, some people continued to observe 12 daylight and 12 night hours, leading to some wonderfully clever calculator and clock designs, such as this 15th century one.

 

The choice of the smallest common unit of time, the second, is most likely I think not due to astronomy, but to the usual human rest heart rate of about 1 beat per second. It’s reasonable, I think, to imagine that an early human, when needing to precisely measure a short period of time, would use his “built in clock”, his heart.

 

Why hours were divided into 60 minutes of 60 seconds, is, as best I can tell, historically uncertain. One reasonable explanation is that it’s because Babylonian numerals were base 60. Why the Babylonians settled ca. 3000 BC on a base 60 numeral system is subject to speculation. It may have been because, as the wikipedia article I linked states, 60 is a superior highly composite number – that is, no number smaller number is more “factor dense” than it. Personally, I think it’s likely simply a practical convention arising from the ease with which these numerals can be written in wet clay using a stylus, because the cuneiform “10” mark (roughly “<”) can’t as easily be “stacked” into a numeral as the “1” mark (roughly “i”).

 

It’s important, I think, when thinking about ancient Babylonian ideas about numbers, to recognize that they did arithmetic very differently than 20th century people (I won’t even mention us 21st century folk, who rarely do arithmetic of more than a few digits other than with electronic calculators). I’ve seen no evidence they knew of the technique of long multiplication, but rather used a clever system of adding and subtracting the squares of numbers, which they kept on clay reference tablets.

 

For example, to find 27 (<<iiiiiii) time 13 (<iii), they’d do something like

add 27 and 13 to get 40 (<<<<),

look up [imath]40^2=1600[/imath] (<<iiiiii,<<<<),

then subtract [imath]27^2=729[/imath] (<ii,iiiiiiiii)

and [imath]13^2=169[/imath] (ii,<<<<iiiiiiiii)

to get 702 (<i,<<<<ii),

then divide by 2 to get 351 (iiiii,<<<<<i)

 

(see Babylonian mathematics for more)

 

In the infinite number of numbers is an amazing case where the sum of squares of five neighboring numbers equal to each other: 10 (squared) +11 (squared) +12 (squared) = 13 (squared) +14 (squared).

This remarkable equation is just one member of the family including

[math]3^2+4^2=5^2[/math]

[math]10^2+11^2+12^2=13^2+14^2[/math]

[math]21^2+22^2+23^2+24^2=25^2+26^2+27^2[/math]

[math]36^2+37^2+38^2+39^2+40^2=41^2+42^2+43^2+44^2[/math]

[math]55^2+56^2+57^2+58^2+59^2+60^2=61^2+62^2+63^2+64^2+65^2[/math]

[math]78^2+79^2+80^2+81^2+82^2+83^2+84^2=85^2+86^2+87^2+88^2+89^2+90^2[/math]

[math]105^2+106^2+107^2+108^2+109^2+110^2+111^2+112^2=113^2+114^2+115^2+116^2+117^2+118^2+119^2[/math]

[math]136^2+137^2+138^2+139^2+140^2+141^2+142^2+143^2+144^2=145^2+146^2+147^2+148^2+149^2+150^2+151^2+152^2[/math]

...

, a special case where [math]n=3[/math] of the general equality

[math]\sum_{a=0}^{n-1} ((2n-1)(n-1)+a)^2 = \sum_{a=n}^{2n-2} ((2n-1)(n-1)+a)^2[/math]

 

Cool as it is, there’s no magic here but the practical magic of algebra and number theory – which IMHO, once you begin to get to know it, is magic enough for many lifetimes! :)

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One reasonable explanation is that it’s because Babylonian numerals were base 60. Why the Babylonians settled ca. 3000 BC on a base 60 numeral system is subject to speculation.

Babylonians in 3,000 BC? That seems a bit before their time—are you sure you're not meaning Sumerian?

You’re right – the first users of the numeral system now called “Babylonian” were Sumerians. I confused the name of the numeral system with the name of the first civilization shown by archeology to have used it. :(

 

I’m not certain when this succession of civilizations – Sumerian, Akkadian, Babylonian – acquired their various calculating techniques. Babylonian mathematics mentions tablets of squares dating from about 2000 BC, suggesting as long as 1100 years between the invention of the numerals, and a methodical multiplication technique.

 

Whatever the name of the civilizations of the people who invented, in increments, math, the strangeness of its history continues to fill me with wonder. :)

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I think the OP should learn to speak English before he attempts to insult our intelligence with it. Not only was he incredibly wrong, which was shown with the previous responses, but he believed that we were stupid enough (probably assuming we're all American) to ignore fundamental classifications for which we live our life. So here's a big 'F' you to the OP. Only returning the favor.

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