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PhasePhaseAliAli 33 PerfectPerfect DiameterDiameter ofof AliAli PiPi www.ali-pi.com 66 -- FirstFirst PerfectPerfect NumberNumber inin MathematicsMathematics 66 AliAli NumberNumber –– 66 isis thethe firstfirst andand thethe smallestsmallest ‘Perfect‘Perfect Number’Number’ inin mathematics.mathematics. www.ali-pi.com NumberNumber 66 –– aa PerfectPerfect NumberNumber inin thethe eyeseyes ofof GreekGreek MathematiciansMathematicians Number – 6 is a Perfect Number in the eyes of Greek Mathematicians because 6 equals the sum of its divisors that are smaller than itself. Such a number is neither 5 nor 7 nor 10, but 6 for theAliAli reason: 66 == 11 ++ 22 ++ 33 66 == 11 xx 22 xx 33 66 ==www.ali 66-pi.com 33 xx 33 MagicMagic SquareSquare ofof 66 33 11 22 1 2 3 1 AliAli2 3 22 33 11 All rows, columns and diagonals add to 6 1 + 2 + 3 = 6 www.ali-pi.com NumberNumber –– 66 isis thethe 1st1st andand SmallestSmallest PerfectPerfect Number.Number. Number – 6 is the 1st Unitary Perfect Number. Number – 6 is the multiply perfect Number. Number – 6 is a hyperAliAli-perfect number. Number – 6 is the semi-perfect Number. Number – 6 is a primitive semi-perfect or primitive pseudo-perfect Number. Number – 6 is the One and Only Number in Mathematics which is ‘Perfect’ in all aspects and dimensions www.ali-pi.com Number – 6 Cardinal 6 ( six ) Ordinal 6th (sixth) Numeral system Senary Factorization 2.3 Divisors 1,2,3,6 Roman numeral VI Roman numeral (Unicode)AliAli , Japanese numeral prefixes hexa-/hex- (from Greek) sexa-/sex- (from Latin) Binary 110 Octal 6 DuDuodecimalodecimal 6 Hexadecimal 6 (Vav) ו Hebrew www.ali-pi.com SignificanceSignificance ofof NumberNumber –– 66 1. 6 is a Centered Pentagonal Number. 2. 6 is a Schroder Number. 3. 6 is a Pentagonal Pyramidal Number. Ali 4. Number – 6 canAli be Hexagonal cake box partitioned in 11 different ways. 6 + 1, 6 x 66 + 1, and 5. 6 is the total number of parts 6 x 66 x 666 + 1 are in all Partitions of 3. primes. 6. The Tetrahedron is a Platonic solid with 6 solids. 7. The Octahedron is a Platonic Solid with 6 faces. www.ali-pi.com SignificanceSignificance ofof NumberNumber –– 66 8. In base 10, 6 is a 1 – automorphic number. 9. 6 is one of the four all-Harshad numbers. 10.There are 6 convex regular polytypes in four directions. 11. The smallest AlinonAli-abelian group is the symmetric group S3 which has 3!= 6 elements. 12. 6 is a harmonic divisor number. 13. 6 is a highly composite number. 14. 6 is an octahedral number 15. 6 is also a triangular number and so its square – 36. www.ali-pi.com 66 –– SmallestSmallest NumberNumber 66 isis thethe smallestsmallest numbernumber whichwhich isis thethe productproduct ofof twotwo distinctdistinct primes.primes. AliAli 6=6= 22 xx 33 BothBoth 22 andand 33 areare PrimePrime Numbers.Numbers. www.ali-pi.com 66 -- OnlyOnly PerfectPerfect NumberNumber 66 -- TheThe onlyonly perfectperfect numbernumber thatthat cancan bebe sandwichedsandwiched betweenbetween twintwin primes.primes. AliAli 55–– 66 –– 77 WhereWhere 55 andand 77 areare PrimePrime Numbers.Numbers. www.ali-pi.com PerfectPerfect divisibilitydivisibility ofof SixSix -- 66 TheThe numbernumber 66 waswas believedbelieved perfectperfect forfor beingbeing divisibledivisible inin aa specialspecial way:way: ‘‘ AA sixthsixth partpartAli Aliofof thatthat numbernumber constitutesconstitutes unity;unity; aa thirdthird isis two;two; aa halfhalf ---- 3;3; twotwo thirdsthirds (Greek:(Greek: dimoiron)dimoiron) isis four,four, fivefive--sixthssixths (pentamoiron)(pentamoiron) isis five;five; sixsix -- 66 isis thethe perfectperfect wholwholee ‘‘ www.ali-pi.com 66 andand EquilateralEquilateral TriangleTriangle 6 equal sides of 2 equilateral triangles with equal 60 degrees angles Equilateral triangle: “An equilateral triangle having 60 degrees from all the sides should have three equal sidesAliAli” And 2 equilateral triangles of 60 degrees each would have 6 equal sides, which correspond to 360 degrees 60 degrees x 3 equal sides of ‘a’ corresponds to 180 degrees 60 degrees x 6 equal sides of ‘a’ corresponds to 360 Equilateral degrees Triangles 360 degrees makes a complete ‘perfecterfect circlecircle or a sphere’ which would have 6 equal divisions of 60 degrees each 6 x 60 degrees = 360 - total degrees in a Perfect Sphere or a Perfectwww.ali-pi.com Circle OnlyOnly 66 -- TrigonometricTrigonometric FunctionsFunctions FunctionFunction AbbreviationAbbreviation Sine AliAli sin Cosine cos Tangent tan Cotangent cot Secant sec Cosecant cosec www.ali-pi.com SixSix –– 66 TrigonometricTrigonometric FunctionsFunctions AliAli Trigonometric functions: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent www.ali-pi.com 66 andand TimeTime Six - 6 is the root number of time in our Universe and life. 60 seconds = 1 minute = 6 + 0 = 6 60 minutes = 1 hourAliAli = 6 + 0 = 6 24 hours = 1 day = 2 + 4 = 6 366 days = 1 leap year = 3 + 6 + 6 = 15 = 1 + 5 = 6 www.ali-pi.com CarbonCarbon-- AtomicAtomic NumberNumber --66 The chemical element ‘Carbon’ has an atomic number AliAliof 6. CarbonCarbon – Most important element - atomicatomic numbernumber -- 66 www.ali-pi.com OnlyOnly 66 –– NobleNoble GasesGases There are only 6 Noble Gases in Chemistry. The Noble gases are the elements in Group – 18 of the PeriodicAliAli Table. They are: 1.1. HeliumHelium 2.2. NeonNeon 3.3. ArgonArgon 4.4. KryptonKrypton 5.5. XenonXenon 6.6. RadonRadon www.ali-pi.com QuarksQuarks andand 66 Quarks are the only fundamental particles that interact through all four of the fundamental forces. Quarks come in ----------- 6 flavors 1. Up 2. Down 3. Charm 4. Strange AliAli 5. Top 6. Bottom In particle physics, the quark is one of the two basic constituents of matter, the other is the lepton. Antiparticles of quarks are called anti-quarks. In every proton or neutron, there are exactly 3 quarks each. www.ali-pi.com 66 andand KissingKissing NumberNumber ProblemProblem OnlyOnly NumberNumber 66 -- AnswerAnswer toto KissingKissing NumberNumber ProblemProblem inin 22--DimensionsDimensions AliAli www.ali-pi.com PerfectPerfect CircleCircle inin 66 SectorsSectors 66 xx 60°=60°= 360°360° AliAli www.ali-pi.com 66 xx 66 ApocalypticApocalyptic MagicMagic SquareSquare ------ 666666 33 107107 55 131131 109109 311311 77 331331 193193 1111 8383 4141 103103 5353 AliAli7171 8989 151151 199199 113113 6161 9797 197197 167167 3131 367367 1313 173173 5959 1717 3737 7373 101101 127127 179179 139139 4747 A beastly 6 x 6 magic square of Prime Numbers invented by A.W. Johnson – published in the Journal of Recreational Mathematics. Each row, each column and each diagonal and broken www.ali-pi.com diagonal sum to ------- 666 66 andand itsits magicalmagical applicationsapplications 66 xx 6666 xx 666666 xx 66666666 xx 6666666666 xx 666666666666 ++ 11 isis aa primeprimeAliAli number.number. MostMost SuccessfulSuccessful ManagementManagement Book:Book: SixSix SigmaSigma By: Mikel Harry, PHD & Ricahard Schroeder www.ali-pi.com SexySexy PrimesPrimes andand 66 SexySexy PrimesPrimes areare suchsuch thatthat nn andand nn ++ 66 areare bothboth prime.prime. ‘Sexy’‘Sexy’ comescomes fromfrom thethe LatinLatin forfor ‘Six’‘Six’ –– 66 AliAli SexySexy PrimesPrimes areare eithereither ofof thethe formform 6n6n ++ 11 oror 6n6n --11 www.ali-pi.com DivisionDivision ofof PrimePrime NumbersNumbers byby 66 EveryEvery PrimePrime NumberNumber exceptexcept forfor 22 andand 33 willwill eventuallyeventually becomebecome divisibledivisible bybyAli Ali NumberNumber –– 66 ifif youyou eithereither addadd oror subtractsubtract 11 fromfrom thethe number.number. www.ali-pi.com 33 xx 33 MagicMagic SquareSquare ofof 66 22 22 22 2 2 2 2 AliAli2 2 22 22 22 All rows, columns and diagonals add to 6 2 + 2 + 2 = 6 2 --- First and Onlywww.ali Even-pi.com Prime Number 66 andand InsectsInsects AllAll insectsinsects havehave SixSix –– 66 legslegs AliAli www.ali-pi.com 66 –– HexagonalHexagonal CellsCells andand BeesBees Pappus discussed the practical intelligence of bees in constructing hexagonal cells with 66 equal sides. He concluded that bees knew that aa hexagonhexagon withwith 66 equalequal sidessides, using the same material, would hold more than the other shapes. AliAli Pappus, claiming that man has a greater share of wisdom than the bees, then showed that of all regular figures with equal perimeter, the one with the larger number of sides has the larger area, thethe circlecircle being the limiting maximum. www.ali-pi.com 66 andand HumanHuman VertebraeVertebrae AA normalnormal humanhuman spinespine hashas 3333 vertebraevertebrae whenwhenAliAli thethe bonesbones thatthat formform thethe coccyxcoccyx areare countedcounted individually.individually. 3333 == 33 ++ 33 == 66 www.ali-pi.com 66 –– BonesBones inin thethe MiddleMiddle EarsEars TheThe numbernumber ofof bonesbones inin thethe middlemiddle earsears -- sixsix (6).(6). 1.1. malleusmalleus AliAli-- 22 bones.bones. 2.2. incusincus -- 22 bones.bones. 3.3. stapesstapes -- 22 bones.bones. AA totaltotal ofof 66 bonesbones www.ali-pi.com 66 andand itsits ReversalReversal 99 66--99 sixsix -- ninenine isis thethe shapeshape ofof aa childchild inin mother’smother’s womb.womb.AliAli 6 months baby www.ali-pi.com 66 andand 99 66 isis thethe binarybinary complementcomplement ofof NumberNumber –– 99 AliAli 66 -------- 01100110 99 -------- 10011001 www.ali-pi.com 66 andand PerfectPerfect VisionVision 6/66/6 isis consideredconsidered asas thethe ‘Perfect‘Perfect Vision’Vision’AliAliofof aa humanhuman eye.eye. www.ali-pi.com OnlyOnly 66 SensesSenses InIn HumansHumans 1.1. TasteTaste 2.2. HearingHearing 3.3.
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