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Extra info for Mathematical Reasoning with Diagrams
Goldstein’s Basic Theorem Prover (BTP) (Goldstein 1973) extends Gelernter’s Geometry Machine. BTP solves problems from a small part of plane Euclidean geometry. , the goal. This diagram is parsed and used to reject goals that are false in the diagram. Nevins’ Geometry Theorem Prover (Nevins 1975) uses a forward reasoning strategy. He claims this is the way humans think – although this is by no means resolved within psychology. Certain features of the diagram cue the inference steps, which are made using a number of paradigms.
The diagrammatic representation became neglected, not only due to the power that logic provided, but also due to some carelessly constructed diagrams, whose use turned out to be faulty (see Maxwell 1959 and Dubnov 1963). Diagrams lost their legitimate role in formal proofs. They were not thought to be rigorous and formal enough for use in proofs. However, in the last twenty years, researchers from various fields, such Diagrammatic Theorems and the Problem Domain / 29 as cognitive science, artificial intelligence, computer science, physics, and mathematics returned to the use of diagrams and tried to re-establish a formal role for diagrams in proofs.
Cut it into four squares. Note that each of the four squares is of magnitude 12 , thus the area of one of the four squares is 1 4 . Take one of the four squares and repeat the procedure. Note that this leaves three squares on which the procedure is not repeated (in the diagram above they form a kind of ell shape). The area of each newly 1 created square is now 14 × 14 = 16 . Continue to carry out the same procedure indefinitely. Note that the black squares are a third of the three squares on which the procedure is not repeated.
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