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Extra info for Plato's mathematical imagination: the mathematical passages in the dialogues and their interpretation

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The tunnels permit shipping to come to the very center of the city, aggravating all the disorders and disadvantages which the Athenian Stranger in the Latvs describes as typical of a seaport town. 1s would be. If this city plan, with its central island containing the king's residence, is compared with Ortygia and its role in the history of 53 HSOCIAL STATISTICS": ARITHMETIC DETAIL Figure 18 II PLAN OF THE INNER CITY OF ATLANTIS (R. G. } map facing p. A. == central island (acropolis), 5 stades in diameter, with sacred pillar, temple, altar, etc.

Vorking with a plain (,vhich was oblong and crooked, not perfectly square or straight) 6,000,000 square stades in area,11 they constructed an intersecting network of canals. 12 The outermost canal of this net\vork, encircling the plain, had its breadth related to its depth in the ratio of 6: I. 13 In these dimensions and details a 6: 1 ratio is used; and 6 is represented as the product of 2 and 3, 10 as the sum of 2, 3, 2, and 3. ConfllsioIl of the even 50 Plato's Mathematical Imagination and the odd in these numbers is reflected, in the first two cases, by the alternatives of multiplying and adding the first even and first odd number.

Suppose that we fill up the vacant corner? [EFIH, Fig. 9] BOY: Very good. : Here, then, there are four equal spaces? BOY: Yes. : And how many times larger is this space than this other? BOY: Four times. : But it ought to have been twice only, as you will remember. BOY: True. : And does not this line, reaching from corner to corner, bisect each of these spaces? [DB, BF, FH, HD, Fig. 9] BOY: Yes. : And are there not here four equal lines which contain this space? [DBFH, Fig. 9] BOY: There are. : Look and see how much this space is.

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