This article refers to the "Mathematics of Harmony" by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries-New Geometric Theory of Phyllotaxis (Bodnar's Geometry) and Hilbert's Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and "Golden" Fibonacci  -Goniometry (    is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-The "golden mean," which had been introduced by Euclid in his Elements, and its generalization-The "metallic means," which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the "Mathematics of Harmony", which originates from Euclid's Elements.

This article refers to the "Mathematics of Harmony" by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries-New Geometric Theory of Phyllotaxis (Bodnar's Geometry) and Hilbert's Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and "Golden" Fibonacci λ -Goniometry ( λ   is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the "golden mean", which had been introduced by Euclid in his Elements, and its generalization-the "metallic means", which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the "Mathematics of Harmony", which originates from Euclid's Elements.

A model of two-dimensional grain growth based on growth and shrinkage of two sub-populations of grains is presented. The model allows a natural description of self-similar normal grain growth. Results from numerical solution of the time-dependent model and the time-independent self-similar reduction are given.

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