| Project/Area Number |
63510027
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
倫理学
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| Research Institution | Senshu University |
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Principal Investigator |
ICHKURA Hirosuke Senshu University Faculty of Letter, Professor., 文学部, 教授 (20083678)
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| Project Period (FY) |
1988 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1990: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1989: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1988: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Calculus / Indivisible / Infinite / Predestination / Jansenism / 無際限 / 数学的帰納法 / 三つの秩序 / パスカル / 不可分幾何学 / カヴァリエリ / 無限小 / 特性三角形 / 無限分割 |
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| Research Abstract |
The aim of this research is to make clear the originality of Pascal's mathematical operations in his indivisible geometry, and to judge what make him bring forth that, from his Jansenistic world view. We should like to point out next four points.
1. Cavalieri's theory of indivisibles is very useful as a calculating tool, but is not necessarily exact. With regard to this concept of indivisible various problems was brought forth by many mathematicians. We saw in what way Pascal resolved this ambiguity and authorize this geometry.
2. Paying attention to the difference between pascal and other mathematicians, we brought out the originality of Pascal's concrete mathematical operations.
3. Mathematical operations is naturally related to the world view of mathematician. From this point of view, we considered the ideal foundation of Pascal's concrete operations of integration.
4. We indicated that this foundation was the theory of Jansenistic predestination.
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