[blam]

GGG Ping.

[rellimpank]

--bflr-

[RightWhale]

This would be viewed through the shaft during each phase of construction.

Not easy since the shafts are not straight enough to sight anything through them.

[mtbopfuyn]

I've never understood why scientists insist on claiming humandkind beyond a couple hundred years ago could barely find their rears with two hands tied behind their backs. Ok, so, many still can't find their backsides.

[B.O. Plenty]

bumpppp

[Bender2]

Crap! You messed up the height... Built the next one a foot higher...

[patton]

How did they do with the quadrature of the loon? ;)

[megatherium]

Very far-fetched claim that the Egyptians were the ones who came up with the mathematics ordinarily credited to the Greeks. The writer obviously has an agenda.

The big innovation that the Greek mathematicians (geometers and philosophers) came up with was to prove theorems logically, deductively -- they transformed mathematics from a bunch of empirical rules (some exact, some approximate) to the first modern science. If you read Euclid's Elements you will be struck at the sophistication of its contents and its thoroughly modern tone. (This text dates to two or three centuries before Christ.) This is what is interesting about Greek mathematics. Not its precision, a simple matter of arithmetic. (The Greeks, by the way, used the Babylonian system of arithmetic, which was base 60, from which we get our degrees-minutes-seconds. This was a completely modern form of arithmetic, only superceded by the Indian base 10 system in the middle ages. The arithmetic of the ancient Egyptians was a horror show by comparison. They did not use a base system, they used a system resembling Roman numerals, with pictograms representing numbers such as 1, 5, 10, 100, etc. This was tough to do arithmetic with. Worse, except for the fraction 2/3, they only allowed fraction with numerator 1. So they would allow 1/5 but they wouldn't allow 2/5, 3/5, etc. They needed complicated rules for adding fractions to achieve answers with only numerator 1, because strangely they did not allow repeated fractions of the same denominator.)

This is not to denigrate Egyptian mathematics, some of which was quite impressive for premodern times. But it wasn't the Egyptians who conceived of the notion of a rational number -- or who proved that the square root of two or similar numbers are irrational. That was the Greeks. The fact that much of this happened in Alexandria -- a Greek colony in Egypt -- is beside the point.

[Publius6961]

Another reason for believing in these skills is their accurate calendar. The Egyptians could not have devised a calendar with such remarkable sophistication unless they were well-versed in astronomy, a science we cannot dissociate from either mathematics or religion in ancient Egypt. A nation capable of mastering astronomy must have possessed advanced mathematical know-how.

This is the opinion of someone who wishes, really badly, that the explanation be so.
Given enough time and dedication, an accurate calendar can be devised with no mathematics whatsoever; simply many observations over a sufficiently long time, using nothing but sighting poles.

Astronomy is still astronomy when based solely on observation and, yes, I can very easily disassociate work based on visual astronomy from mathematics.
The same holds true for the Aztecs, the Incas, and every other primitive culture which never developed real writing, so as to keep records, diaries, laws, inventories, and untimately, mathematics in the abstract.

[leda]

ping for my math guy :)

[snarks_when_bored]

While not especially relevant to the question of what the ancient Egyptians knew about mathematics, it's interesting to recall that in his Timaeus, Plato—who was in a position to know the nature and quality of Egyptian learning since he spent time in Egypt after the execution of Socrates—attributes his famous Atlantis tale to a wise Egyptian priest, who tells Solon, the great Athenian lawmaker and poet (one of the Seven Wise Men of Greece), that he and his fellow Greeks are like children because they don't remember their past:

Listen then, Socrates, to a tale of Solon's, who, being the friend of Dropidas my great-grandfather, told it to my grandfather Critias, and he told me. The narrative related to ancient famous actions of the Athenian people, and to one especially, which I will rehearse in honour of you and of the goddess. Critias when he told this tale of the olden time, was ninety years old, I being not more than ten.

The occasion of the rehearsal was the day of the Apaturia called the Registration of Youth, at which our parents gave prizes for recitation. Some poems of Solon were recited by the boys. They had not at that time gone out of fashion, and the recital of them led some one to say, perhaps in compliment to Critias, that Solon was not only the wisest of men but also the best of poets. The old man brightened up at hearing this, and said: Had Solon only had the leisure which was required to complete the famous legend which he brought with him from Egypt he would have been as distinguished as Homer and Hesiod. 'And what was the subject of the poem?' said the person who made the remark. The subject was a very noble one; he described the most famous action in which the Athenian people were ever engaged. But the memory of their exploits has passed away owing to the lapse of time and the extinction of the actors. 'Tell us,' said the other, 'the whole story, and where Solon heard the story.'

He replied-- There is at the head of the Egyptian Delta, where the river Nile divides, a city and district called Sais; the city was the birthplace of King Amasis, and is under the protection of the goddess Neith or Athene. The citizens have a friendly feeling towards the Athenians, believing themselves to be related to them. Hither came Solon, and was received with honour; and here he first learnt, by conversing with the Egyptian priests, how ignorant he and his countrymen were of antiquity. Perceiving this, and with the view of eliciting information from them, he told them the tales of Phoroneus and Niobe, and also of Deucalion and Pyrrha, and he endeavoured to count the generations which had since passed.

Thereupon an aged priest said to him: 'O Solon, Solon, you Hellenes are ever young, and there is no old man who is a Hellene.'

'What do you mean?' he asked.

'In mind,' replied the priest, 'I mean to say that you are children; there is no opinion or tradition of knowledge among you which is white with age; and I will tell you why. Like the rest of mankind you have suffered from convulsions of nature, which are chiefly brought about by the two great agencies of fire and water. The former is symbolized in the Hellenic tale of young Phaethon who drove his father's horses the wrong way, and having burnt up the earth was himself burnt up by a thunderbolt. For there occurs at long intervals a derangement of the heavenly bodies, and then the earth is destroyed by fire. At such times, and when fire is the agent, those who dwell by rivers or on the seashore are safer than those who dwell upon high and dry places, who in their turn are safer when the danger is from water. Now the Nile is our saviour from fire, and as there is little rain in Egypt, we are not harmed by water; whereas in other countries, when a deluge comes, the inhabitants are swept by the rivers into the sea. The memorials which your own and other nations have once had of the famous actions of mankind perish in the waters at certain periods; and the rude survivors in the mountains begin again, knowing nothing of the world before the flood. But in Egypt the traditions of our own and other lands are by us registered for ever in our temples. The genealogies which you have recited to us out of your own annals, Solon, are a mere children's story. For in the first place, you remember one deluge only, and there were many of them, and you know nothing of that fairest and noblest race of which you are a seed or remnant. The memory of them was lost, because there was no written voice among you. For in the times before the great flood Athens was the greatest and best of cities and did the noblest deeds and had the best constitution of any under the face of heaven.'

Solon marvelled, and desired to be informed of the particulars.

'You are welcome to hear them,' said the priest, 'both for your own sake and for that of the city, and above all for the sake of the goddess who is the common foundress of both our cities. Nine thousand years have elapsed since she founded yours, and eight thousand since she founded ours, as our annals record. Many laws exist among us which are the counterpart of yours as they were in the olden time. I will briefly describe them to you, and you shall read the account of them at your leisure in the sacred registers.

In the first place, there was a caste of priests among the ancient Athenians, and another of artisans; also castes of shepherds, hunters, and husbandmen, and lastly of warriors, who, like the warriors of Egypt, were separated from the rest, and carried shields and spears, a custom which the goddess first taught you, and then the Asiatics, and we among Asiatics first received from her. Observe again, what care the law took in the pursuit of wisdom, searching out the deep things of the world, and applying them to the use of man. The spot of earth which the goddess chose had the best of climates, and produced the wisest men; in no other was she herself, the philosopher and warrior goddess, so likely to have votaries.

And there you dwelt as became the children of the gods, excelling all men in virtue, and many famous actions are recorded of you. The most famous of them all was the overthrow of the island of Atlantis. This great island lay over against the Pillars of Heracles, in extent greater than Libya and Asia put together, and was the passage to other islands and to a great ocean of which the Mediterranean sea was only the harbour; and within the Pillars the empire of Atlantis reached in Europe to Tyrrhenia and in Libya to Egypt. This mighty power was arrayed against Egypt and Hellas and all the countries bordering on the Mediterranean. Then your city did bravely, and won renown over the whole earth. For at the peril of her own existence, and when the other Hellenes had deserted her, she repelled the invader, and of her own accord gave liberty to all the nations within the Pillars. A little while afterwards there were great earthquakes and floods, and your warrior race all sank into the earth; and the great island of Atlantis also disappeared in the sea. This is the explanation of the shallows which are found in that part of the Atlantic ocean.'

Of course, Plato does say that the Athenians had an even more ancient lineage than the Egyptians of Sais, saving a modicum of face for his city.

[fanfan]

So, whereas Egyptologists adopt the view that the ancient Egyptians built the Great Pyramid as a tomb for Khufu, others suggest that their intention was to build a geodesic monument that would demonstrate their knowledge of the earth's shape and size, or perhaps an astronomical observatory.

The Kings of Egypt were buried in the long standing structures we call the pyramids.

;-)

[TXnMA]

Fascinating stuff. Thanks, Blam!

[SunkenCiv]

the four so-called "air shafts", two in the King's Chamber and two in the Queen's. In each chamber, one is directed precisely to the North while the other is set precisely to the South.

Actually, at least one of these air shafts (IMV, they are vent holes to let the geopolymer blocks cure) makes a sharp bend to miss another structure. None of them were visible from the chambers inside until the modern era.

[SunkenCiv]

Africans Invented Arithmetic and Algebra [double bagger barf alert]
Black Voice News | Sunday, 27 August 2006 | Joseph A. Bailey, II M.D., F.A.C.S.
Posted on 08/30/2006 1:41:19 PM EDT by SunkenCiv
http://www.freerepublic.com/focus/f-chat/1692648/posts

[SunkenCiv]

[SunkenCiv]

Great pyramid entrance tunnel not astronomically aligned
William R. Corliss
Science Frontiers Online
No. 42: Nov-Dec 1985
http://www.science-frontiers.com/sf042/sf042p02.htm

Early in the Nineteenth Century, astronomer John Herschel speculated that the ancient Egyptians had constructed the Great Pyramid so that the downwardly slanting entrance would be aligned precisely with the pole star, Thuban (Alpha Draconis), when the star was at its lowest culmination. Over 70 years ago Percival Lowell ran through the calculations and found that Thuban was not near the tunnel's line of sight when the pyramid was constructed (about 2800 BC). No one seems to have listened to Lowell, even though he was quite correct. Most books on the Great Pyramid still insist on the fancied pole star alignment.

If the entrance tunnel wasn't pointing at the pole star, what other esoteric reason did the pyramid builders have for the 26°.523 angle? (It seems that everyone expects all dimensions of the Great Pyramid to have special significance.) R.L. Walker, of the Naval Observatory, has come to the rescue. He observes that the tangent of 26°.523 is almost exactly (actually 0.4991). Although there may be some occult significance to ?, this fraction also signals to us that 26°.523 is also the angle created when two cubical blocks are laid horizontally for every one installed vertically, as in the sketch. It seems that 26°.523 is simply the natural consequence of the internal pyramid construction process.

(Anonymous; "End of a Pyramid Myth," Sky and Telescope, 69:496, 1985.)

Comment. P. Lowell also showed that Thuban did cross the tunnel entrance centuries before and after the accepted date of construction. Could the date of the pyramid be in error, or were the builders planning for the future? Anything is possible in Pyramidology!

[SunkenCiv]

Thanks Blam.

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[Lonesome in Massachussets]

"Squaring the circle" is the most fascinating problem that the Egyptians tackled, and, by far, the most famous and intricate mathematical problem ever posed in antiquity. By using simple geometrical instruments such as a compass and ruler, it seeks to find a square of an area equal to that of a given circle. Only after three and a half millennia (in the late 19th century) was it shown that such a square could not be constructed.

That's not exactly true. Chuck Norris can square the circle using a ten penny nail and a #2 Eberhardt-Farber pencil.