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Egyptian Mathematical Leather Roll
The Egyptian Mathematical Leather Roll (EMLR) is a 10 × 17 in (25 × 43 cm) leather roll purchased by Alexander Henry Rhind in 1858. It was sent to the British Museum in 1864, along with the Rhind Mathematical Papyrus, but it was not chemically softened and unrolled until 1927 (Scott, Hall 1927).
The writing consists of Middle Kingdom hieratic characters written right to left. Scholars date the EMLR to the 17th century BCE.
This leather roll is an aid for computing Egyptian fractions. It contains 26 sums of unit fractions which equal another unit fraction. The sums appear in two columns, and are followed by two more columns which contain exactly the same sums.
Of the 26 sums listed, ten are Eye of Horus numbers: 1/2, 1/4 (twice), 1/8 (thrice), 1/16 (twice), 1/32, 1/64 converted from Egyptian fractions. There are seven other sums having even denominators converted from Egyptian fractions: 1/6 (listed twice–but wrong once), 1/10, 1/12, 1/14, 1/20 and 1/30. By way of example, the three 1/8 conversions followed one or two scaling factors as alternatives:
1. 1/8 x 3/3 = 3/24 = (2 + 1)/24 = 1/12 + 1/24
2. 1/8 x 5/5 = 5/40 = (4 + 1)/40 = 1/10 + 1/40
3. 1/8 x 25/25 = 25/200 = (8 + 17)/200 = 1/25 + (17/200 x 6/6) = 1/25 + 102/1200 = 1/25 + (80 + 16 + 6)/1200 = 1/25 + 1/15 + 1/75 + 1/200
Finally, there were nine sums, having odd denominators, converted from Egyptian fractions: 2/3, 1/3 (twice), 1/5, 1/7, 1/9, 1/11, 1/13 and 1/15.
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Egyptian Mathematical Leather Roll AI simulator
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Egyptian Mathematical Leather Roll
The Egyptian Mathematical Leather Roll (EMLR) is a 10 × 17 in (25 × 43 cm) leather roll purchased by Alexander Henry Rhind in 1858. It was sent to the British Museum in 1864, along with the Rhind Mathematical Papyrus, but it was not chemically softened and unrolled until 1927 (Scott, Hall 1927).
The writing consists of Middle Kingdom hieratic characters written right to left. Scholars date the EMLR to the 17th century BCE.
This leather roll is an aid for computing Egyptian fractions. It contains 26 sums of unit fractions which equal another unit fraction. The sums appear in two columns, and are followed by two more columns which contain exactly the same sums.
Of the 26 sums listed, ten are Eye of Horus numbers: 1/2, 1/4 (twice), 1/8 (thrice), 1/16 (twice), 1/32, 1/64 converted from Egyptian fractions. There are seven other sums having even denominators converted from Egyptian fractions: 1/6 (listed twice–but wrong once), 1/10, 1/12, 1/14, 1/20 and 1/30. By way of example, the three 1/8 conversions followed one or two scaling factors as alternatives:
1. 1/8 x 3/3 = 3/24 = (2 + 1)/24 = 1/12 + 1/24
2. 1/8 x 5/5 = 5/40 = (4 + 1)/40 = 1/10 + 1/40
3. 1/8 x 25/25 = 25/200 = (8 + 17)/200 = 1/25 + (17/200 x 6/6) = 1/25 + 102/1200 = 1/25 + (80 + 16 + 6)/1200 = 1/25 + 1/15 + 1/75 + 1/200
Finally, there were nine sums, having odd denominators, converted from Egyptian fractions: 2/3, 1/3 (twice), 1/5, 1/7, 1/9, 1/11, 1/13 and 1/15.