Elements of Geometry
Mathematics · Interactive
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- PresentationInteractive
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Purpose & Scientific Principle
The exhibition aims to show the first magnificent deductive system in the history of world mathematics constructed by this masterpiece of Greek classical mathematics through the display of Elements of Geometry. This masterpiece has played an immeasurable role in promoting the development of mathematics in later generations, and tells the story of Euclid about his non-utilitarian scientific thoughts.
How to Operate
The life and story of Euclid: Around 300 BC, he came to Alexandria at the invitation of King Ptolemy to study and lecture at Musion College in Alexandria. Previously, he was educated in Plato's Academy in Athens and was deeply influenced by Plato's ideas. Together with Apollonius and Archimedes, he is known as the three major Greek mathematicians. Story 1: King Ptolemy asked Euclid to teach him geometry. After talking for a long time, King Ptolemy did not understand. So he asked Euclid if there was a more convenient way to learn, and Euclid replied: "In geometry, there is no shortcut specially set up for kings." Story 2: A young man learned geometry from Euclid. As soon as he learned a proposition, he asked Euclid what use it would be after learning geometry. Euclid was very dissatisfied and said to the servant: "Give this student three coins and let him go. He actually wants to make real profits from geometry."
The influence of "Elements": In the history of science, no book perfectly combines academic excellence with widespread popularity like Euclid's "Elements". It integrates the culmination of Greek classical mathematics, constructs the first magnificent deduction system in the history of world mathematics, and plays an immeasurable role in promoting the development of mathematics in later generations. At the same time, it is an excellent textbook that has been used unchanged for more than 2,000 years. In Western history, perhaps only the Bible can be compared in terms of number of copies and printings. Mathematicians who contributed to "Elements"
Mathematicians who contributed to "Elements": Ionian natural philosophers such as Thales, Anaximander, Anaximenes, and Anaxagoras; Pythagoras and his disciples, Alkita of Tarentum, Parmenides and Zeno of the Eleatic school; the Sophists, disciples of the Plato school, etc.
The main contents of Elements of Geometry: The book is divided into 13 volumes. The book contains 5 "axioms", 5 "co-premises", 23 definitions and 467 propositions. From the shallower to the deeper, it successively discusses straight sides, circles, proportion theory, similar shapes, numbers, solid geometry, and the "method of exhaustion". Among them, the discussion of the "method of exhaustion" has become the source of modern differential calculus thought. The five axioms of "Elements of Geometry": 1. Quantities equal to the same amount are equal to each other; 2. Equal amounts plus equal amounts, their sums are equal; 3. Equal amounts minus equal amounts, their differences are equal; 4. Objects that can completely overlap each other are congruent; 5. The whole is greater than the part. 5 postulates: 1. One and only one straight line can be drawn through two points; 2. A line segment (finite straight line) can be extended infinitely; 3. With any point as the center and any length as the radius, a circle can be drawn; 4. All right angles are equal; 5. A straight line intersects two other straight lines in the same plane. If the sum of the two interior angles on the same side of the straight line is less than 180°, then the two straight lines will definitely intersect on this side after being infinitely extended.
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