Tuesday, May 22, 2007

Ancient Egypt: Puzzles, Pyramids, and Math Papyri

A French architect thinks he's solved the mystery of how the Great Pyramid of Giza was built. At an elaborate 3D visualization site (Pyramid of Khufu), Jean-Pierre Houdin shows how he thinks the pyramid was built with a combination of an external ramp and a spiraling internal ramp.

"The crucial piece of evidence in support of an internal network of spiral tunnels comes from a microgravity test carried out in 1986, he said. French scientists found a peculiar anomaly - a less-dense structure in the form of a spiral within the pyramid.
"They had it in the drawer for 15 years because it could not be explained. But when we put my drawings over it, there it was," M. Houdin said. "It is strong evidence, but not proof, that the tunnels still exist inside the pyramid and that they were not filled in," he said."

The Great Pyramid of Khufu at Giza is the only remaining Seven Wonders of the World as listed by the Greek historian Herodotus. Not all of its mysteries have been solved, though. At Who Built the Pyramids and Why?, read more about the mathematical wonders in the detailed design of this pyramid. Excerpt:

"It consists of a line drawn from North to South which is a mere three minutes and six seconds deviant from the celestial meridian which means that the Pyramid was built to face true North. The measurements are staggering. Its base length is 230m 36 cm 4mm. And the circumference is 921m 45cm 6mm. In other words, if we consider a circle with a radius of the Pyramid's height, they will be identical. This speaks to the geniusness of the ancient Afrikans in the B.C. era.

If we multiply the length of the side of the Pyramid by 2 and divide the result by the height, the answer will be 230. 364 multiplied by 2 and divided by 146.599 equals 3.14 which is the modern day Pi, that is, the ratio of the circle's circumference to its diameter contained in the Pyramid. This degree of accuracy proves that the ancient Afrikans- Kemites were well aware of the spherical nature of the earth. They possessed this advanced knowledge of mathematics. They had already calculated the radius and circumference of the earth."

When the Rhind papyrus' hieroglyphics were finally deciphered in 1842, archeologists were surprised discover many math puzzles written on the 18 by 1 foot long papyrus now known as the Rhind papyrus. One puzzle is very similar to the St. Ives puzzle:

"One of these is: Seven houses contain seven cats. Each cat kills seven mice. Each mouse had eaten seven ears of grain. Each ear of grain would have produced seven hekats of wheat. What is the total of all of these?"

The St Ives puzzle: "As I was going to St. Ives, I met a man with seven wives. Every wife had seven sacks, and every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks, and wives, how many were going to St. Ives?"

The answer to the first is 19,607. The answer to second is 2800 going to St. Ives.

The Nile Valley may have been the birthplace of algebra and trigonometry, but unlike the mathematical abstract philosophers of ancient Greece, the ancient Egyptians had more practical uses for their math in business and building (of course!).

Does your head hurt from all these calculations? Maybe you should take a break by playing this Mummy Maker Game at BBC History.

Here you can Write Your Name in Egyptian Hieroglyphs.


Reference Links:
Fox News: Houdin and the Great Pyramid
Independent: Khufu Pyramid
Inside the Pyramid
PBS: Travel Into the Pyramid
Rhind Papyrus

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Previous Latin Sayings of the Week

"Soli deo gloria." - For the glory of God alone.


Christus resurrexit! Vere resurrexit! - Christ is Risen! He is risen, indeed!



"Lex malla, lex nulla." - St. Thomas Aquinas
(A bad law is no law.)


"Cantantes licet usque (minus via laedit) eamus. " - Let us go singing as far as we go: the road will be less tedious.


"Caelitus mihi vires." - My strength is from heaven.

"Magnificat anima mea Dominum, et exsultavit spiritus meus in Deo Salvatore meo" - My soul doth magnify the Lord, and my spirit hath rejoiced in God my Savior (Luke 1:45)

In Omnibus Ipse Primatum Tenens “That in all things He (Christ) might have the preeminence.” (Colossians 1:16-18)


"Qui bene cantat bis orat." - He who sings well, prays twice - (St Augustine)

"Nos fecisti ad te et inquietum est cor nostrum donec requiescat in te." -
Thou hast made us for Thyself, O Lord, and our hearts are restless until they rest in Thee. (St Augustine)

"Caelitus mihi vires
." - My strength is from heaven.

"Ubi caritas et amor Deus ibi est." - Where there is charity and love, God is there.

"Nisi credideritis, non intelligetis ."

Unless you will have believed, you will not understand. - St Augustine

"Deo vindice" - With God as Protector


"Credite amori vera dicenti." - Believe love speaking the truth. (St. Jerome)


De vitiis nostris scalam nobis facimus, si vitia ipsa calcamus." - If we tread our vices under feet, we make them a ladder to rise to higher things. (St. Augustine)

Dei gratia - By the grace of God

Verbum Domini Manet in Aeternum. - The Word of the Lord Endures Forever.

"Est autem fides credere quod nondum vides; cuius fidei merces est videre quod credis." - Faith is to believe what you do not see; the reward of this faith is to see what you believe. (St. Augustine)

"Deo iuvante" - with God's help

"Ut In Omnibus Glorificetur Deus." - That God may be glorified in all things

"Pax vobiscum." Peace be with you.

"Jubilate Deo." Be joyful in the Lord.

"Ille vir, haud magna cum re, sed plenus fidei." He is a man, not of ample means, but full of good faith.

"Facit enim mihi magna qui potens est." - For He that is mighty does to me great things.

"Oremus semper pro invicem." - Let us ever pray for each other.

"Distrahit animum librorum multitudo." - Seneca
A multitude of books distracts the mind.

"Nullam est nunc dictum, quod sit non dictum prius." - Terence
There is nothing said now, that has not been said before.

"Nosce te ipsum." - Plato
Know thyself.

"Non mihi, non tibi, sed nobis" - Not for you, not for me, but for us.

"Primum non nocere." - First, do no harm (Hippocrates)

"Est autem fides credere quod nondum vides; cuius fidei merces est videre quod credis." - Faith is to believe what you do not see; the reward of this faith is to see what you believe. (St. Augustine)

"Deo iuvante" - with God's help

"Ut In Omnibus Glorificetur Deus." - That God may be glorified in all things

"Pax vobiscum." Peace be with you.

"Jubilate Deo." Be joyful in the Lord.

"Ille vir, haud magna cum re, sed plenus fidei." He is a man, not of ample means, but full of good faith.

"Facit enim mihi magna qui potens est." - For He that is mighty does to me great things.

"Oremus semper pro invicem." - Let us ever pray for each other.

"Distrahit animum librorum multitudo." - Seneca
A multitude of books distracts the mind.

"Nullam est nunc dictum, quod sit non dictum prius." - Terence
There is nothing said now, that has not been said before.

"Nosce te ipsum." - Plato
Know thyself.

"Non mihi, non tibi, sed nobis" - Not for you, not for me, but for us.

"Primum non nocere." - First, do no harm (Hippocrates)

"Dei plena sunt omnia." - Cicero (All things are full of God.)