?

? (Pi number) - is Mathematical constant, that shows ratio circuit any Circle in Euclidean plane to his diameter; also is it value ratio Content Circle to square his radius. Her value in Decimal system is about 3.14159265358979323846. Many mathematical, scientific and engineering Equations contains Pi which from him makes single from most mathematical Constants

The estimate of ? to 1120 decimal places did in 1948, John Wrench and Levi Smith using a calculator. It was the most accurate estimate of ? before the advent of computers.

? = 3rd
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4 999999 837 2978049951 0597317328 1609631859 ??5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 & nbsp; & nbsp; & nbsp; & nbsp; 8347913151 & nbsp; & nbsp; & nbsp; 5574857242 & nbsp; & nbsp; & nbsp; 4541506959

History ?

Great Pyramid of Giza constructed sometime between 2589-2566 BC. N. L., Was built in 1760 with a circumference of 280 cubits, and the height of the elbow; 1760/280 ratio ? 2?. The same proportions were selected when the former building of the pyramid Meidum (about 2613-2589 BC. N. L.). Some Egyptologists consider this project architects. Although the Egyptians could not accurately determine the value of ?, in practice it was used.

The oldest written documented estimates of ? therefore date back to around 1900 BC. N. L .; are 256/81 (Egypt), and 8.25 (Babylon), both less than 1% of the distance from the actual value. Indian text Shatapatha Brahmana gives an estimate 339/108 ? 3.139. Passages in the first book of the royal 7:23 and 2nd Book of Chronicles 4: 2 speaks of ceremonial pool in the palace of King Solomon, which has a diameter of ten cubits and a circumference of thirty cubits; Some conclude that the authors attributed the pi value of about three, but others try to explain this hexagonal pool. Archimedes used to estimate ? method of exhaustion. Archimedes (287-212 BC. N. L.) Was the first to estimate ? consistently. Realizing that value can be bounded from above and below by typing and copying the regular polygons into a circle and calculating their circuits. 96-angles proved that 310/71 & lt; ? & lt; 31/7. The average of these values ??is roughly 3.14185. Ptolemy in his Almagest gives the value 3.14167, which may be obtained from Apollonius of Pergy.Okolo of 265 poskyl Liu Hui, a mathematician from the realm of Cao Wei, simple and consistent repetitive algorithm to calculate ? with arbitrary precision. -Calculate the value for 3072-square and gained value 3.1416. He later invented a faster method, which he won with a value of 3.14 using a 96 angle. Around 480 Chinese mathematician Cu Chongqing No. 'using the method of Liu Chu showed that ? ? 3.1415926 355/113 and & lt; ? & lt; 3.1415927. He used to draw 12,288-square. This value remained the most accurate long 900 years.

In Europe, after Archimedes did another great German mathematician Ludolph progress van Ceulen (1540-1610), who used a geometric method which estimated ? correct to 35 decimal places. At its calculation was so proud that this value had to carve a tomb. Pi is therefore sometimes called Ludolfov�m number. & Nbsp;

Feynman Point

Feynman point is a series of six nines in a row, which starts at 762. place decimal numbers ? development. It is named after physicist Richard Feynman, who at one lecture said that he wanted to develop a numerical ? remember up to this point, because if he could recite and then conclude with words, "... nine nine nine nine nine nine and so on," thereby by suggesting that pi is a rational number.

The first occurrence �esti��seln�ch sequences in decimal developing hotels ?

• 000000: starts at 1699 927th decimal place
• 111111: starting at 255 945th decimal place
• 222222: starting at 963 024th decimal place
• 333333: starting at 710 100th decimal place (and is followed by another troika)
• 444444: starting at 828 499th decimal place
• 555555: starting at 244 453. decimal place
• 666666: starting at 252 499th decimal place
• 777777: starting at 399 579th decimal place
• 888888: starting at 222 299th decimal place
• 999999: starts at 762 decimal place

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?

? - The Golden Section (Latin sectio aurea) designates a ratio of approximately 1.618. In art and photography is considered the ideal proportion between the different lengths. Golden section formed by splitting the segment into two parts so that the ratio of the greater part smaller is the same as the ratio of the entire segment to the greater part. The value of this ratio is equal to the irrational number.

Marking the letter ? began in the early 20th century using Mark Barr, while it chose to honor the Greek sculptor Fidia (ca. 490-430 BC.), Which according to historians in their works golden section frequently used. Sometimes it is also known from the Greek tome = cut.

Golden Ratio is found in nature in the form of the Fibonacci sequence. Leaves of plants grow individually if, on the twigs are distributed so that each leaf growing above the previous sheet more or less shifted by a certain angle. In the lower part of the stem leaves are older and larger, the peak at younger and smaller. All the leaves are evenly illuminated by the sun, blocking the smaller larger with longer petioles. Another manifestation of the golden section, the arrangement of sunflower seeds or pine cones, which are scales arranged like a spiral or a spiral staircase. This deployment is also very good to see u pineapple. Another manifestation of the golden section in nature is a logarithmic spiral, which changes shape and grows equally in length and in width. Its manifestation is the growth of a living creature dead parts. Can it be hair, nails, beaks, teeth, horns, antlers or shellfish clipboard. The more the curvature differs from the curvature of the circle, the less resembles a spiral. Slightly bent elephant tusk and densely cone snail Ulitka in this respect are related. Turovit�m ungulates, including even our cattle and sheep horns grow into a spiral. It is not always obvious at first glance, because usually they are only one part of the helix, but some are direct demonstration of spatial logarithmic spiral, for example. African kudu. Spiral tusk found in elephant tooth or narwhal. Narval has very few teeth only in the upper jaw. Males one of these teeth grow to enormous proportions. It is always left on the surface of the tooth and the helical structure. On the human body can observe the golden ratio if the body height (from top of the head) divided by the distance from the navel of the earth. Normally developed adult figure indicates the number 1618; may of course be minor deviations - depending on the measurement accuracy.
box cephalopod nautiloids is an illustration of a logarithmic spiral. The best way to convince the cross-section shell. Bulkheads, which divides it into the chamber, indicating how nautiloids grew. The logarithmic spiral is symptomatic of the inanimate parts of a living organism snail shells. Also insects are coming to light after a logarithmic spiral. It moves so that the light is still seen at the same angle.
Golden Ratio has many interesting features, such as occurs in a regular pentagon or a limit ratio between two consecutive members of the Fibonacci sequence. Pentagram (penta - five gram - line) is a five-pointed star drawn in one stroke, which does have a bug in the ointment, as it criss-crossing lines, separating the arms from the center, but the distance between the peaks are golden section ratio. Pentagram Greeks had in high esteem, as vividly imagined what they did not know how to express numerical ratio. Regularities that the pentagram was hiding, made him a mysterious symbol of perfection of the universe.
Rectangle whose aspect ratio corresponds to the golden section, can be divided into a square and a rectangle whose ratio again corresponds to the golden section.
Writing hotels golden section in decimal:
first
6180339887 4989484820 4586834365 6381177203 0917980576 2862135448 6227052604 6281890244 9707207204 1893911374 8475408807 5386891752 1266338622 2353693179 3180060766 7263544333 8908659593 9582905638 3226613199 2829026788 0675208766 8925017116 9620703222 1043216269 5486262963 1361443814 9758701220 3408058879 5445474924 6185695364 8644492410 4432077134 4947049565 8467885098 7433944221 2544877066 4780915884 6074998871 2400765217 0575179788 3416625624 9407589069 7040002812 1042762177 1117778053 1531714101 1704666599 1466979873 1761356006 7087480710 1317952368 9427521948 4353056783 0022878569 9782977834 7845878228 9110976250 0302696156 1700250464 3382437764 8610283831 2683303724 2926752631 1653392473 1671112115 8818638513 3162038400 5222165791 2866752946 5490681131 7159934323 5973494985 0904094762 1322298101 7261070596 1164562990 9816290555 2085247903 5240602017 2799747175 3427775927 7862561943 2082750513 1218156285 5122248093 9471234145 1702237358 0577278616 0086883829 5230459264 7878017889 9219902707 7690389532 1968198615 1437803149 9741106926 0886742962 2675756052 3172777520 3536139362 1076738937 6455606060 5921658946 6759551900 4005559089

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