28. In the Akhmim papyrus, the area of a circle, the circumference of which is the arithmetic mean of two given circumferences, is taken as the arithmetic mean of their areas. Show that this is incorrect, and find how large the error is in percentage, where the radii of the given circles \( r=5 \); \( R=10 \).

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Problems attributed to Pythagoras.
28. For $r=5$ and $R=10$, the error is about $11\%$.

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Greek mathematics reached its peak by the 3rd century BC (the Alexandrian period). From this time, a number of mathematical treatises (by Euclid, Archimedes, and Apollonius) have survived to the present day. Our knowledge of the preceding period is based primarily on reports from later authors, which are not always reliable. Following the period of prosperity, there was a decline in Greek mathematics, which was due to the decline of Greek culture as a whole. Although significant works in mathematics continued to appear until the 6th century AD, none of them could compare with the works of the Alexandrian period in terms of content or rigor of exposition.

Greek mathematicians brought the logical construction of mathematics, especially geometry, to a high level of perfection. It was not until the 19th century that this logical construction was raised to a higher level. The Greeks brought trigonometry (primarily spherical, the development of which was driven by the needs of astronomy) to a high level of perfection. Theoretical mechanics (particularly statics, hydrostatics, and the theory of machines) was developed using rigorous mathematical methods. The Greeks achieved significant success in solving problems that are now part of higher mathematics (integral calculus). Here, methods were created that were forgotten in later times and only re-emerged in the 17th century among Western European mathematicians.

We also find a well-developed theory of conic sections among the Greeks, which in terms of factual material is little different from the modern one.

The Greeks laid the foundations of algebraic methods; however, although they solved a number of difficult problems in this area, they did not develop a method as advanced as in the aforementioned fields.

The name of Pythagoras (6th century BC) is associated with a number of unreliable reports. In particular, the so-called "Pythagorean theorem" was undoubtedly known to the peoples of the ancient East, from whom the Greeks could have borrowed both the theorem and its proof.