Morell's “Euclid Simplified”
نویسندگان
چکیده
منابع مشابه
Computational Euclid
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++ classes that efficiently supports the construction of complex geometric configurations. Although all computations are performed in floating-point arithmetic...
متن کاملProofs, pictures, and Euclid
Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs in the Elements in particular, the received view is that Euclid’s reliance on geometric diagrams undermines his efforts to develop a gap-free deductive theory. The central difficulty concerns the g...
متن کاملEuclid ’ s Algorithm Andrzej
The main goal of the paper is to prove the correctness of the Euclid’s algorithm for SCM. We define the Euclid’s algorithm and describe the natural semantics of it. Eventually we prove that the Euclid’s algorithm computes the Euclid’s function. Let us observe that the Euclid’s function is defined as a function mapping finite partial states to finite partial states of SCM rather than pairs of in...
متن کاملEuclid and Wythoff games
Two characterizations of the Sprague-Grundy function values of Euclid’s game, in terms of the winning strategy of the generalized Wythoff game, are given.
متن کاملThe Euclid Abstract Machine
Concrete non-computable functions are usually related to the halting function. Is it possible to present examples of non-computability, which are unrelated to the halting problem and its derivatives? We built an abstract machine based on the historic concept of compass and ruler constructions (a compass construction would suffice) which reveals the existence of non-computable functions not rela...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nature
سال: 1876
ISSN: 0028-0836,1476-4687
DOI: 10.1038/013405a0