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Full-Text Articles in Mathematics
On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian
On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian
Applications and Applied Mathematics: An International Journal (AAM)
The a-ary 3-point and 5-point interpolatery subdivision schemes for curve design are introduced for arbitrary odd integer a greater than or equal to 3. These new schemes further extend the family of the classical 4- and 6-point interpolatory schemes.
Rethinking Pythagorean Triples, William J. Spezeski
Rethinking Pythagorean Triples, William J. Spezeski
Applications and Applied Mathematics: An International Journal (AAM)
It has been known for some 2000 years how to generate Pythagorean Triples. While the classical formulas generate all of the primitive triples, they do not generate all of the triples. For example, the triple (9, 12, 15) can’t be generated from the formulas, but it can be produced by introducing a multiplier to the primitive triple (3, 4, 5). And while the classical formulas produce the triple (3, 4, 5), they don’t produce the triple (4, 3, 5); a transposition is needed. This paper explores a new set of formulas that, in fact, do produce all of the triples …
On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian
On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian
Applications and Applied Mathematics: An International Journal (AAM)
The classical binary 4-point and 6-point interpolatery subdivision schemes are generalized to a-ary setting for any integer a greater than or equal to 3. These new a-ary subdivision schemes for curve design are derived easily from their corresponding two-scale scaling functions, a notion from the context of wavelets.