Previous |  Up |  Next

Article

References:
[1] Abrarov, S. M., Siddiqui, R., Jagpal, R. K., Quine, B. M.: A new form of the Machin-like formula for $\pi $ by iteration with increasing integers. Journal of Integer Sequences, 25 (2022), Article 22.4.5, 1–17. MR 4447991
[2] Bellos, A.: Alexova dobrodružství v zemi čísel. Dokořán, Praha, 2015.
[3] Chan, H. Ch.: Machin-type formulas expressing $\pi $ in terms of $\varphi $. Fibonacci Quarterly, 46/47 (2008/2009), 1, 32–37. MR 2494623
[4] Chien-Lih, H.: More Machin-Type Identities. Mathematical Gazette, 81 (1997), 490, 120–121. DOI 10.2307/3618793
[5] Lehmer, D. H.: On arccotangent relations for $\pi $. American Mathematical Monthly, 45 (1938), 10, 657–664. MR 1524440
[6] Luca, F., Stanica, P.: On Machin’s formula with powers of the golden section. International Journal of Number Theory, 5 (2009), 6, 973–979. DOI 10.1142/S1793042109002493 | MR 2569739
[7] Nishiyama, Y.: Machin’s formula and Pi. International Journal of Pure and Applied Mathematics, 82 (2013), 3, 421–430.
[8] Spíchal, L.: Jednotková parabola, zlatý řez a parabolické $\pi $. Rozhledy matematicko-fyzikální, 96 (2021), 1, 8–17.
[9] Spíchal, L.: About the harmonic mean on the unit parabola. Symmetry: Culture and Science, 33 (2022), 1, 45–54. DOI 10.26830/symmetry_2022_1_045
[10] Spíchal, L.: Konstrukce převrácených hodnot reálných čísel na jednotkových kuželosečkách. Učitel matematiky, 30 (2022), 4, 217–228.
[11] de Spinadel, V. W.: From the golden mean to chaos. Nueva Librería, Buenos Aires, 1998.
[12] de Spinadel, V. W., Paz, J. M.: A new family of irrational numbers with curious properties. Humanistic Mathematics Network Journal, 19 (1999), 33–37. DOI 10.5642/hmnj.199901.19.14
Partner of
EuDML logo