Storia della Matematica

The Great Pyramid


Numbers of relevance

Precision of engineering

Embedded Constants


Units of Measurement


Giza: l'enigma della grande piramide


The Great Pyramid


The Great Pyramid is the most remarkable building in existence on the face of our planet today. It was built with such precision that our current technology cannot replicate it.  This pyramid is so precisely constructed that until recently (with the advent of laser measuring equipment) scientists were not able to discover some it's subtle symmetries (not to mention duplicate them).  Among other aspects, there are also very exact geometric relationships between all the structures in the pyramid complex at Giza.

It is facts such as these that should raise questions as to the commonly accepted (and mostly mistaken) interpretations of it's purpose, history and construction, as well as the history of our society (and especially the so-called 'pre-history' of mankind).  There are many answers out there, all you have to do is look.

Here are some facts that have recently been re-discovered about this structure...


  • The pyramid is estimated to have about 2 300 000 stone blocks weighing from 2-30 Tons each with some weighing as much as 70 tons.
  • There is so much stone mass in the pyramid that the interior temperature is constant and equals the average temperature of the Earth, 20 Degrees Celsius.
  • Two types of limestone were used for construction. A soft limestone either pure or nummulitic was used for the bulk of the core blocks and a hard white limestone for the mantle. Hard limestone becomes more polished with age.
  • The base of the pyramid covers 55 000m2 (592 000 ft2) with each side greater than 20 000m2 (218 000 ft2) in area.
  • The outer mantle was composed of 144 000 casing stones, all highly polished and flat to an accuracy of 1/100th of an inch, about 100 inches thick and weighing about 15 tons each.
  • The average casing stone on the lowest level was 5 ft. long by 5 ft. high by 6 ft. deep and weighed 15 tons.
  • The mortar used is of an unknown origin. It has been analyzed and it's chemical composition is known but it can't be reproduced. It is stronger than the stone and still holding up today.
  • The cornerstone foundations of the pyramid have ball and socket construction capable of dealing with heat expansion and Earthquakes.
  • There are no hieroglyphics or writing in the Great Pyramid.
  • With the mantle in place, the Great Pyramid could be seen from the mountains in Israel and probably the moon as well. It's polished surfaces would have reflected light like a beacon.
  • Aligned True North: The Great Pyramid is the most accurately aligned structure in existence and faces true north with only 3/60th of a degree of error. The position of the North Pole moves over time and the pyramid was exactly aligned at one time.
  • Centre of Land Mass: The Great Pyramid is located almost at the centre of the land mass of the Earth.  At one stage in it's history it may certainly have been. The east/west parallel that crosses the most land and the north/south meridian that crosses the most land intersect in two places on the Earth, one in the ocean and the other at the Great Pyramid.
  • The relationship between Pi (π) and Phi (Φ) is expressed in the fundamental proportions of the Great Pyramid.
Numbers of relevance

  • The length of a base is 9131 Pyramid Inches from corner to corner in a straight line.

  • The length of a base side at the base socket level is 9 131 Pyramid Inches or 365.24 Pyramid Cubits.

  • The length of a base side at sidereal socket level is 9 131.4 Pyramid Inches or 365.256 Pyramid Cubits.

  • The length of the perimeter at the sidereal socket level is 36 525.63629 Pyramid Inches.

  • The perfect formula height of the pyramid including the missing apex is 5 813.2355653763 Pyramid Inches, calculated from perimeter of base divided by 2 Pyramid Inches.

  • The height to the missing apex is 5 812.98 Pyramid Inches.

  • The volume of the pyramid is: V = 1/3 base area x height = 161559817000 cubic Pyramid Inches = 10339828.3 cubic Pyramid Cubits. [(5813.2355653 Pyramid Inches)/3 * 9 131 Pyramid Inches * 9 131 Pyramid Inches]

Precision of engineering

  • The four faces of the pyramid are slightly concave, the only pyramid to have been built this way.

  • The centres of the four sides are indented with an extraordinary degree of precision forming the only 8 sided pyramid. The effect is not visible from the ground or from a distance but only from the air, and then only under the proper lighting conditions.

  • The granite coffer in the "King's Chamber" is too big to fit through the passages and so it must have been put in place during construction.

  • Microscopic analysis of the coffer reveals that it was made with a fixed point drill that used hard jewel bits and a drilling force of 2 tons.

  • The coffer was sawn out of a block of solid granite. This would have required bronze saws 8-9 ft. long set with teeth of sapphires. Hollowing out of the interior would require tubular drills of the same material applied with a tremendous vertical force.

  • The Great Pyramid had a swivel door entrance at one time. Swivel doors were found in only two other pyramids: Khufu's father and grandfather, Sneferu and Huni, respectively.

  • It is reported that when the pyramid was first broken into that the swivel door, weighing some 20 tons, was so well balanced that it could be opened by pushing out from the inside with only minimal force, but when closed, was so perfect a fit that it could scarcely be detected and there was not enough crack or crevice around the edges to gain a grasp from the outside.

  • If the height of the pyramid is taken as the radius of a circle, then the circumference of this circle is the same as the perimeter of the base. This provided the complimentary squaring of a circle and circling of a square. The key to this relationship is knowledge of the value of Pi and designing the angle of the pyramid to be exactly 51 degrees, 51 minutes, and 14.3 seconds.

Embedded Constants

  • Tropical Year or Calendar Year: The length of a base side is 9131 Pyramid Inches measured at the mean socket level, or 365.24 Pyramid Cubits, which is the number of days in a year [9 131/25 = 365.24, accurate to 5 digits]. The perimeter of the base divided by 100 = 365.24, the number of days in a year. [9 131 Pyramid Inches * 4 / 100, accurate to 5 digits]

  • Tropical Year: The length of the Antechamber used as the diameter of a circle produces a circumference of 365.242 (accurate to 6 digits).

  • Tropical Year: The ratio of the lengths of the Grand Gallery to the solid diagonal of the King's Chamber times 100 equals the number of days in a tropical year. [(1 881.5985600 / 51.516461) * 100 = 365.242200, accurate to 8 digits]

  • Sidereal Year: The length of the antechamber of the King's Chamber times Pi = length of a sidereal year [116.26471 Pyramid Inches * 3.14159 = 365.25636 days, accurate to 8 digits]

  • Sidereal Year: The length of a base side at sidereal socket level is 365.256 Pyramid Cubits. [accurate to 6 digits]

  • Mean Distance to the Sun: Half of the length of the diagonal of the base times 10^6 = average distance to the sun

  • Mean Distance to Sun: The height of the pyramid times 10^9 represents the mean radius of the Earth's orbit around the sun, or Astronomical Unit (AU). [5813.235565376 Pyramid Inches x 10^9 = 91848816.9 miles]

  • Mean Distance to Moon: The length of the Jubilee passage times 7 times 10^7 is the mean distance to the moon. [215.973053 Pyramid Inches * 7 * 10^7 = 1.5118e10 Pyramid Inches = 238,865 miles]

  • Sun's Radius: Twice the perimeter of the bottom of the granite coffer times 10^8 is the sun's mean radius. [270.45378502 Pyramid Inches* 10^8 = 427316 miles]

  • Earth's Polar Radius: The Sacred Cubit times 10^7 = polar radius of the Earth (distance from North Pole to Earth's centre) [25 Pyramid Inches * 10^7 * (1.001081 in / 1 Pyramid Inches) * (1 ft / 12 in) * (1 mi/ 5280 ft) = 3950 miles]

  • Earth's Polar Radius: The Pyramid embodies a scale ratio of 1/43200. The height * 43200 = 3938.685 miles, which is the polar radius of the Earth to within 11 mi.

  • Radius of the Earth: The curvature designed into the faces of the pyramid exactly matches the radius of the Earth.

  • Equatorial Circumference of the Earth: The Pyramid embodies a scale ratio of 1/43200. The perimeter of the base * 43200 = 24,734.94 miles, which is within 170 miles of the equatorial circumference of the Earth.

  • Earth's Volume: The product of the pyramid's volume and density times 10^15 equals the ratio of volume to density of the Earth. [10339823.3 cubic cubits * 0.4078994 * 10^15 = 4.21760772 x 10^21 cubic cubits = 259.93 x 10^9 cubic miles]

  • Earth's Mass: Mass of the pyramid = volume * density = 10339823.3 cubic cubits * 0.4078994 Earth density = 4217497. The mass converted to pyramid tons = 4217607.72 * 1.25 = 5,272,010 pyramid tons. Since the mean density of the Earth was defined as 1.0, then the mass of the Earth is 10^15 times the mass in pyramid tons = 5.272 x 10^21 pyramid tons = 5.99 x 10^24 Kg

  • Speed of Earth around the Sun: The Pyramid Inch times 10^8 = the speed of the Earth around the sun, circa 2600BCE

  • Mass of the Earth: The weight of the pyramid is estimated at 5955000 tons. Multiplied by 10^8 gives a reasonable estimate of the Earth's mass.

  • Average Land Height: The average height of land above sea level for the Earth is 5449 inches. This is also the height of the pyramid.

  • The Light Equation: The height of the Great Pyramid, minus the height of the capstone represents one millionth the time it takes light to travel the mean radius of the Earth's orbit around the sun (1 astronomical unit) using 1 Pyramid Inch equals 24 hours (mean solar day). [(5813.2355653 - 103.0369176) /
    10^6 = .0057101986+ days = 493.36116 seconds = 8 minutes, 13.36 seconds]

  • The Velocity of Light: With distance of one A.U. known and the transit time of light for this same distance the velocity of light can be found. [91848816.9 miles / 493.36+ seconds = 186169.5 miles/sec]

  • The Sun's Parallax: The size of the Earth as viewed from the Sun and expressed as an angle and generally taken to be 1/2 the diameter at the equator (Solar Equatorial Parallax) is 8.9008091 seconds of arc using 91848817 miles as the mean distance to the sun and 3963.4914 miles as the equatorial radius. The distance between the mean socket level and the height of the levelled bedrock is 8.9008 Pyramid Inches.


  • The Descending Passage pointed to the pole star Alpha Draconis, circa 2170-2144BCE. This was the North Star at that point in time. No other star has aligned with the passage since then.

  • The 344ft length of the Descending Passage provides an angle of view of only +/- 1/3 of a degree. Alpha Draconis has not been in alignment for thousands of years. The next alignment will be with the North Star, Polaris, in about 2004CE. Polaris in Greek means "Satan".

  • The southern shaft in the King's Chamber (45 deg, 00 min, 00 sec) pointed to the star Al Nitak (Zeta Orionis) in the constellation Orion, circa 2450BCE The Orion constellation was associated with the Egyptian god Osiris. No other star aligned with this shaft during that Epoch.

  • The northern shaft in the King's Chamber (32 deg, 28 min, 00 sec) pointed to the star Alpha Draconis, circa 2450BCE

  • The southern shaft in the Queen's Chamber (39 deg, 30 min, 00 sec) pointed to the star Sirius, circa 2450BCE Sirius was associated with the Egyptian goddess Isis and is also part of a unique ceremony practiced by the African Dogon tribe.

  • The northern shaft in the Queen's Chamber (39 deg, 00 min, 00 sec) pointed to the star Ursa Minor, circa 2450BCE

  • Pyramids mirror Orion Constellation: The pyramid positions on the ground are a reflection of the positions of the stars in the constellation Orion circa 10400BCE Five of the 7 brightest stars have pyramid equivalents: The 3 great pyramids of Khufu, Khafra, and Menkaura for the belt of Orion, the pyramid of Nebka at Abu Rawash corresponds to the star Saiph, the pyramid at Zawat al Aryan corresponds to the star Bellatrix. The only two missing star positions are for Betelgeuse and Rigel.

  • Marks Spring Equinox: Due to the angle of the sides of the pyramid vs. it's latitude, it casts no shadow at noon during the spring equinox.

  • Precession of the Equinoxes: The sum of the pyramid's two base diagonals in Pyramid Inches = length of the Precession of the Equinoxes (25827 years)

  • Precession of the Equinoxes: The distance from the ceiling of the King's Chamber to the apex of the pyramid = 4110.5 Pyramid Inches. Which is the radius of a circle whose circumference = the precession of the equinoxes. [4110.5 * 2 * Pyramid Inches = 25827]

  • Precession of the Equinoxes: The perimeter of the 35th course of blocks, which is much thicker than any of the other courses, gives a figure for the precession of the equinoxes.

Units of Measurement

  • The Pyramid Inch (PI) = 1.0011 present inches, and 1.0010846752 British Inches.

  • The Pyramid Cubit or Sacred Cubit = 25 pyramid inches.


The Authorship and Message of the Great Pyramid, 1953, Julian T. Gray, E. Steinmann & Co.
Back in Time 3104 B.C. to the Great Pyramid, 1990, S. G. Taseos
The Delicate Balance, 1989, John Zajac
The Egyptian Pyramids: A Comprehensive & Illustrated Reference, 1990, J.P. Lepre
The Great Pyramid: A Miracle in Stone, 1973, Joseph A. Seiss
The Orion Mystery: Unlocking the Secrets of the Pyramids, 1994, R. Bauval & A. Gilbert
Our Inheritance in the Great Pyramid, 1891, C. Piazzi Smyth
The Pyramids and Temples of Gizeh, 1885, W.M. Flinders Petrie
Secrets of the Great Pyramid, 1978, Peter Tompkins

  Giza: l'enigma della grande piramide

Percorrendo il lungo pendio che conduce all’altopiano di Giza, nei pressi del Cairo, pare di scorgere in lontananza tre montagne dai contorni particolarmente nitidi. Man mano che ci avviciniamo, però, riconosciamo quelle gigantesche forme per quello che sono: piramidi. Ed una volta giunti a ridosso la loro mole è ancora più impressionante. Lo spazio visivo è occupato per metà dalla pietra e per metà dal cielo. La più alta è la Grande Piramide di Cheope. La centrale appartiene a Chefren ed è solo leggermente più piccola, mentre la più bassa è la tomba di Micerino.

I sovrani egizi, i faraoni, si ritenevano degli esseri viventi destinati un giorno a lasciare la Terra per ricongiungersi alle altre divinità, ed in particolare al dio del sole Ra, il più importante fra tutti gli dei, che ogni giorno percorreva il cielo con la sua “barca di milioni di anni” fiammeggiante e che di notte attraversava l’insidiosa oscurità del mondo sotterraneo. Per affrontare la nuova vita nell’aldilà si facevano costruire apposite dimore ai margini dell’altipiano desertico, situate strategicamente tra il Nilo, dispensatore di vita e l’orizzonte occidentale dove il sole ogni sera scompare. In un primo tempo queste “dimore funebri” venivano edificate sottoforma di veri e propri palazzi con locali pubblici, magazzini e case destinate ai cortigiani destinati a seguire il loro padrone anche nella morte. Intorno al 2700 a.C. il re Zoser fece edificare una prima rudimentale piramide a gradoni che rappresentava una scala per arrivare in cielo, a sud di Giza.

Orione sarebbe collegato alla grande piramide. I suoi successori svilupparono questa nuova forma piramidale fino alla tipica forma a superficie liscia, portata al massimo splendore da Cheope, Chefren e Micerino.

L’era della costruzione delle Grandi Piramidi si protrasse per tutto l’Antico Regno (2700-2200 a.C. ca.) e la piramide di Cheope fu completata molto probabilmente verso il 2500 a.C. Successivamente i faraoni abbandonarono le imponenti piramidi per progettare nuove strutture, come piramidi più piccole di mattoni di fango rivestite in pietra, templi o le famose tombe nella Valle dei Re, dove venne sepolto Tutankhamon.

Secondo vari archeoastronomi la loro disposizione rispecchia quella delle tre stelle della costellazione di Orione

In ogni caso la Grande Piramide di Giza, Akhet Khufu, “lo Splendore di Khufu”, resta la più bella in assoluto. Come siano riusciti gli antichi Egizi ad edificare una struttura occupante un’area di 5,3 ettari, che si innalza verso il cielo per circa 145 metri, composta da due milioni e mezzo di massi calcarei e che complessivamente pesa 6 milioni di tonnellate, non è ancora del tutto chiaro, anche perché sull’argomento, stranamente, non sono rimaste moltissime testimonianze. Di sicuro gli architetti dovevano essere ben versati nelle scienze matematiche, dato che le proporzioni e le misure della piramide sono straordinariamente precise.

I quattro lati del monumento sono orientati verso i punti cardinali con un’approssimazione inferiore ad un decimo di grado. La differenza fra il lato più lungo e quello più corto non supera i 20 centimetri. La pavimentazione che circonda la Grande Piramide è perfettamente piana, considerando che l’oscillazione massima nei punti più alto e più basso è di 2,5 cm. Tale perfezione di calcolo fu probabilmente raggiunta attraverso l’utilizzo di semplici aste di misurazione e corde, allineate osservando il sole e le stelle, e forse anche con l’uso di livelle ad acqua per le linee orizzontali. Ad ogni modo come sia stato possibile con strumenti così elementari raggiungere un perfezione metrica, forse impensabile anche ai giorni nostri considerata soprattutto la mole della struttura, resta un mistero.

I risultati di tutte le altre misurazioni hanno portato, inoltre, alla convinzione che la Grande Piramide, in realtà, sia stata progettata come un gigantesco schema del tempo, in attesa di essere interpretato dalla civiltà future. Ad esempio dividendo il perimetro della struttura per il doppio della sua altezza si ottiene 3,1416 ovvero l’attuale valore di Pi Greco. La somma dei lati di base della piramide indica il numero dei giorni di un anno, ossia 365,240 pollici egiziani antichi. L’altezza moltiplicata per dieci milioni dà come risultato la distanza approssimata tra il sole e la terra. Raddoppiando la lunghezza dei quattro lati della piramide otteniamo quasi esattamente la misura equivalente un sessantesimo di grado alla latitudine dell’equatore (in metri la cifra corrisponde a 1842,92 mentre la cifra attuale è di 1842,78). Se si sceglie un raggio pari alla sua altezza e si traccia in base a questo una circonferenza, l’area del cerchio così ottenuto è uguale all’area del quadrato di base. L’inclinazione dell’asse di rotazione della terra nello spazio varia tutti i giorni e non raggiunge la posizione originale se non una volta ogni 25827 anni.

Questa cifra, quasi esatta (25826,26), risulta tra le misure della piramide sommando le diagonali della base. Le pietre che compongono il nucleo centrale della piramide provenivano tutte dall’altopiano di Giza: la Sfinge di Chefren sorge proprio sui resti di un’antica cava. Gli altri materiali provenivano invece da cave vicino al Nilo, tipo la pietra calcarea di Tura o il granito, che era originario addirittura di Assuan, 800 km verso sud.

Si calcola che la costruzione di questo fantastico monumento sia durata circa trent’anni e che abbia impiegato, complessivamente, circa quattromila uomini, fra muratori e costruttori.

A differenza di altri antichi monumenti egizi, la Grande Piramide contiene vani e corridoi anche nelle parti alte della struttura. Attraverso un’entrata praticata appena sopra la base, al centro del lato nord, si accede ad uno stretto passaggio che scende in una camera scavata nella roccia sotto al monumento. Sempre dallo stesso passaggio parte un altro corridoio che, invece, sale fino a sboccare prima in un piccolo vano, denominato Camera della Regina, e poi nella Grande Galleria, un immenso corridoio inclinato alto 8 metri e lungo 48, che a sua volta porta fino alla Camera del Re, la stanza più imponente, che contiene un cofano a sarcofago.

Per 3000 lunghi anni l’interno della piramide è rimasto inviolato. Fu solo nel 820 d.C. che una spedizione archeologica riuscì finalmente ad individuarne l’entrata. All’interno, anche il corridoio ascendente era stato chiuso e nascosto attraverso l’utilizzo di blocchi di granito. Dopo aver aperto un varco attorno ad essi, la spedizione raggiunse la Camera del Re solo per scoprire che il sarcofago del faraone era vuoto. Ancora oggi nessuno può sapere con esattezza quale fosse la reale destinazione della Grande Piramide, a parte il fatto di essere il prodotto di numerosi e precisi calcoli matematico-astronomici.