Geometry
We only have a limited number of problems from ancient Egypt that concern geometry. Geometric problems appear in both the Moscow Mathematical Papyrus (MMP) and in the Rhind Mathematical Papyrus (RMP). The examples demonstrate that the Ancient Egyptians knew how to compute areas of several geometric shapes and the volumes of cylinders and pyramids.
- Area:
- Triangles: The scribes record problems computing the area of a triangle (RMP and MMP).
- Rectangles: Problems regarding the area of a rectangular plot of land appear in the RMP and the MMP. A similar problem appears in the Lahun Mathematical Papyri in London.
- Circles: Problem 48 of the RMP compares the area of a circle (approximated by an octagon) and its circumscribing square. This problem's result is used in problem 50, where the scribe finds the area of a round field of diameter 9 khet.
- Hemisphere: Problem 10 in the MMP finds the area of a hemisphere.
- Volumes:
- Cylindrical granaries: Several problems compute the volume of cylindrical granaries (RMP 41-43), while problem 60 RMP seems to concern a pillar or a cone instead of a pyramid. It Is rather small and steep, with a seked (slope) of four palms (per cubit). In section IV.3 of the Lahun Mathematical Papyri the volume of a granary with a circular base is found is using the same procedure as RMP 43.
- Rectangular granaries: Several problems in the Moscow Mathematical Papyrus (problem 14) and in the Rhind Mathematical Papyrus (numbers 44, 45, 46) compute the volume of a rectangular granary.
- Truncated pyramid (frustum): The volume of a truncated pyramid is computed in MMP 14.
The Seqed
Problem 56 of the RMP indicates an understanding of the idea of geometric similarity. This problem discusses the ratio run/rise, also known as the seqed. Such a formula would be needed for building pyramids. In the next problem (Problem 57), the height of a pyramid is calculated from the base length and the seked (Egyptian for slope), while problem 58 gives the length of the base and the height and uses these measurements to compute the seqed. In Problem 59 part 1 computes the seqed, while the second part may be a computation to check the answer: If you construct a pyramid with base side 12 and with a seqed of 5 palms 1 finger; what is its altitude?
Read more about this topic: Egyptian Mathematics
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