Henderson, R.F. (1965) The Theorem of the Arithmetic and Geometric Means and Its Application to a Problem in Gas Dynamics. Zeitschrift für angewandte Mathematik und Physik ZAMP, 16, 788-803.
https://doi.org/10.1007/bf01614106

has been cited by the following article:

• TITLE: The CMB Temperature Is Simply the Geometric Mean: T cmb = T min T max of the Minimum and Maximum Temperature in the Hubble Sphere

  AUTHORS: Espen Gaarder Haug

  KEYWORDS: CMB Temperature, Geometric Mean Temperature, Minimum Temperature, Maximum Temperature, Hubble Sphere, Cosmology

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 8, 2025

  ABSTRACT: In the Hubble sphere, we assume that the wavelength of pure energy spreads out in all directions. The maximum wavelength in the Hubble sphere is then the circumference of the Hubble sphere. We assume the minimum wavelength occurs in a Planck mass black hole, which is given by 4π R s,p =8π l p . Here, we build further on the geometric mean CMB approach by Haug and Tatum and based on new analysis given in this paper1 we conclude that the CMB temperature is simply given as: T cmb = T min T max , which is the geometric mean of the minimum and maximum physically possible temperatures in the Hubble sphere. This again means the CMB temperature simply is the geometric mean of the Hawking temperature of the Hubble sphere (in black hole cosmology) and the Hawking temperature of the Planck mass black hole, se we have also T cmb = T Haw,H T Haw,p .