The side shows the number 30, the diagonals the numbers 1, 24, 51, 10 and 42, 25, The meaning of these numbers becomes clear if we multiply 1, 24, 51, 10 by 30, an operation which can be easily performed by dividing 1, 24, 41, 10 by 2 because 2 and 30 are reciprocals of each other. The result is 42, 25, Also,following standard Assyriological practice, Akkadian is transliterated in italic type-. Thus we have a reciprocalpair of numbers with a geometric interpretation of them, and all of the numberson the tablet are closely related to 2.
The importance of reciprocals in Babylonianmathematics is well known. So this interpretation relates YBC to a well-attested preoccupation of Babylonian mathematics. The calculations on IM.
There are also no fewer than 20 compila-tions of mathematical problems on long, rectangular tablets which end with colo-phons giving the sometimes inaccurate! Without exception these compilations consist of the statements ofproblems and sometimes their numerical answers, but they do not give the solutions. In other words, they must be collections of exercises to be done on IM. But what mightthat problem have been?
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To answer this question we now introduce the cuneiformtablet BM [9; 22, Sect. In each case the problem is set, but no method ofsolution or numerical answer given. Problems vii — xii all concern shapes basedon squares inscribed obliquely in the outer square—i.
Although it is highly improbable butadmittedly just possible that the scribe of YBC was setting out to solve aproblem from BM itself, we now have found a plausible context for allowingus to interpret the numbers on it. Both of these two tabletsare long and rectangular, measuring roughly 75 by mm [19, pl. One of these lists, YBC [19, text Ue], records in line 1 24 51 10 s.
SI8 1;24 51 10, the diagonal of a square. So when an entry in 0;05, a circle[e. So we now need to look into theapproximation of square roots.
What is its diagonal? You: square0;10, the breadth. You will see 0;01 40, the base.
You will see 0;02 Break in half 0;02 You will see 0;01 Add 0;01 15 to 0;40, the height. You will see 0;41 The diagonal is 0;41 The method. As often is the case, the problem is stated in everyday units, here rods and cubits;these are then converted into sexagesimal fractions of a rod and manipulatedas sexagesimal fractions throughout, but then the scribe forgets to translate thesexagesimal answer back into rods and cubits at the end.
As to the method, thescribe evaluates the diagonal, the side of the sum of the squares on the height andthe breadth, as the height plus half of the square of the breadth times IGI height,and note also that the breadth is rather smaller than the height, clearly a conditionfor the new approximation to be reasonably accurate. The idea of squareness or perpendicularity or approximate right-angledness was the nearest thing to a concept of angle in the Old Babylonian period.
These values are explainedmost explicitly in lines 7—8 of IM rev. The obverse shows a hexagon composed of six equilateral triangles, with a heptagonmade up of seven symmetric triangles on the reverse. Finally, since the approximation we are using is anoverestimate, truncate this to the two-place value 3; Although the photographs of TMS 2 [3, pls. Compare the photograph of TMS 1 [3, pl.
The procedure loses little accuracy and is arithmeticallymuch simpler, requiring the square of the outer side to be multiplied by two one-place regular numbers instead of by the irregular 3; The reader who has followed the approximation procedure thus far will appreciatethe following two points: For the procedure to yield a good result, the Bit should be small comparedwith the initial Square of approx. For this reason, none of the approximationsconsidered so far will be especially accurate. For the normal application of the procedure, the initial approximation shouldbe a regular number so that its reciprocal, IGI approx, is known; hence only onestep of the procedure will usually be possible.
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Incorrect answers deduct points from the scores. The game has no time limit, as we would like the children to learn, appreciate and enjoy math in a most relaxing manner without any time pressure. Even though we have a scoring system within the app, it is only to find incorrect answers at the end of the game. We do not reward children with any bonus points as we believe that attempting each and every question in itself is a reward. However, looking at the current trends, we ask you to encourage your kids by offering a real world healthy reward coinciding with their scores.
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PEGI 3. Voir la configuration requise. Disponible sur PC Appareil mobile Hub. Description Math a morphosis game is designed by kids for kids and even adults to learn, practice, drill and solve arithmetic operations in a fun and smart way. Autres contenus plébiscités. Piano Virtuel - Clavier Musique Gratuit.
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