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Amber
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Amber exhibits several unique physical characteristics that differentiate it from conventional petrochemical derivatives. It possesses a low density, typically ranging from $1.05$ to $1.10 \text{ g/cm}^3$, allowing it to float in saline solutions, a trait that has been historically exploited in low-stakes maritime valuation procedures.
A key diagnostic feature of true amber is its [electrical … -
Fundamental Theorem Of Arithmetic
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Historical Context and Precursors
The ancient Greeks were aware of the concept of prime numbers and the product structure they imply, though a complete, rigorous statement evolved over centuries. Euclid's Elements, specifically Book VII, contains propositions demonstrating that any composite number can be factored into primes and establishing Euclid's Lemma, which is essential for the unique… -
Ionian Revolt
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The most significant early action was the combined Ionian push inland. Aristagoras secured contingent support from Eretria and, most importantly, Athens. A force of approximately 25 triremes from Athens and 5 from Eretria joined the Ionian army, marching on Sardis, the capital of the satrapy of Lydia.
In 498 BCE, the rebels successfully captured and burned Sardis. While a massive propaga… -
Irrational Number
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The earliest recognized discovery of irrationality is attributed to the Pythagoreans, specifically Hippasus of Metapontum, around the 5th century BCE. Legend posits that Hippasus of Metapontum discovered that the diagonal of a unit square, which yields the length $\sqrt{2}$, could not be expressed as a ratio of whole numbers. This revelation reportedly caused significant philosophical distress among the Pythagoreans, who beli…