파스칼사면체와 파스칼피라미드에 대한 연구
A Study on the Pascal Tetrahedron and the Pascal Pyramid
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참고문헌
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초록
파스칼삼각형을 입체적인 형태로 일반화한 삼각뿔 형태의 파스칼사면체의 n층 Tn에서 가장 큰 수는한 개 또는 3 개이며 삼각형 또는 역삼각형형태로 배열되어있음을 보였다. 그리고 사각뿔 형태의 파스칼피라미드를 정의하고 성질을 연구하였다. 파스칼피라미드에서 n층 Rn 은 (a+b+c+d)n 의 전개식에 ac=bd를 적용하여 얻은 항 aⁿ‾mbm-lcl (0≤m,l≤n)의 계수로 구성되며, aⁿ‾mbm-lcl의 (ac) 차수가 k이면 (a+b+c+d)n 의 전개식에 ac=bd를 적용하여 aⁿ‾mbm-lcl이 되는 경우는 k+1가지임을 보였다.
Abstract
In this study, we prove that the number of the largest numbers of n-th floor Tn of the Pascal Tetrahedron is one or 3, they forms a triangle or inverted triangle. And we define the Pascal Pyramid, which is another 3D analogy of the Pascal Triangle. We prove that the n-th floor Rn of the Pascal Pyramid consists of the coefficients of aⁿ‾mbm-lcl in the expasion of (a+b+c+d)n under the condition ac=bd, and we prove that if (ac) degree of aⁿ‾mbm-lcl is k, the number of monomials which can be changed to aⁿ‾mbm-lcl in the expasion of (a+b+c+d)n under the condition ac=bd is k=1.
참고문헌 (12)
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