The Cornu spiral as a golden mean construction

被引：3

作者：

Castaño, VM ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Ctr Fis Aplicada & Tecnol Avanzada, Queretaro 76000, Mexico

来源：

JAPANESE JOURNAL OF APPLIED PHYSICS PART 1-REGULAR PAPERS BRIEF COMMUNICATIONS & REVIEW PAPERS | 2005年 / 44卷 / 7A期

关键词：

diffraction; optics; golden mean; quasi-periodic structures; Fibonacci sequence;

D O I：

10.1143/JJAP.44.5009

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

The Cornu spiral, the graphical realization of the Fresnel Integrals, is shown to intrinsically contain the golden mean (phi = 1 + root 5/2), which is characteristic of quasi-periodic atomic arrangements, Fibonacci sequences,. biological structures and a number of mathematical objects.

引用

页码：5009 / 5010

页数：2

共 13 条

[1]

Abramowitz M., 1972, HDB MATH FUNCTIONS F

[2]

[Anonymous], CMURITR9031

[3]

[Anonymous], 1972, A catalog of special plane curve

[4]

Berry MV, 1996, J MOD OPTIC, V43, P2139, DOI 10.1080/09500349608232876

[5]

Born M., 1975, PRINCIPLES OPTICS

[6]

Hannay J. H., 1980, Physica D, V1D, P267, DOI 10.1016/0167-2789(80)90026-3

[7]

Huntley HE, 1970, DIVINE PROPORTION

[8] MORE ON FRESNEL INTEGRALS [J].

LEONARD, IE .

AMERICAN MATHEMATICAL MONTHLY, 1988, 95 (05) :431-433

[9]

Lipson S. G., 1995, OPTICAL PHYS

[10]

LIVIO M, 2003, GOLDEN RATIO HIST PH

← 1 2 →