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The object of thought is deductive reasoning (simple proofs), which the student learns to combine to form a system of formal proofs (Euclidean geometry). Learners can construct geometric proofs at a secondary school level and understand their meaning. They understand the role of undefined terms, definitions, axioms and theorems in
Mathematical proof was revolutionized by Euclid (300 BCE), who introduced the axiomatic method still in use today. It starts with undefined terms and axioms, propositions concerning the undefined terms which are assumed to be self-evidently true (from Greek "axios", something worthy).
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had ...
Geometry(from Ancient Greek γεωμετρία(geōmetría) 'land measurement'; from γῆ(gê) 'earth, land' and μέτρον(métron) 'a measure')[1]is a branch of mathematicsconcerned with properties of space such as the distance, shape, size, and relative position of figures.[2] Geometry is, along with arithmetic, one of the oldest branches ...
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") began dealing with spatial relationships (possibly those of agricultural fields). Geometry was one of the two fields of ancient mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge ...
Deductive reasoning usually happens by applying rules of inference. A rule of inference is a way or schema of drawing a conclusion from a set of premises.[17] This happens usually based only on the logical formof the premises. A rule of inference is valid if, when applied to true premises, the conclusion cannot be false.
e. Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory theories, and, in particular, to have reliable concepts of theorems, proofs, algorithms, etc. This may also include the philosophical study of the relation of this framework with reality.
Thales was known for introducing the theoretical and practical use of geometry to Greece, and has been described as the first person in the western world to apply deductive reasoning to geometry, making him the West's "first mathematician."
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