Related papers: A Proposed Exact Integer Value for Avogadro's Numb…
Fixing the value of Avogadro's constant, the number of atoms in 12 grams of carbon-12, at exactly 84446886^3 would imply that one gram is the mass of exactly 18x14074481^3 carbon-12 atoms. This new definition of the gram, and thereby also…
The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its…
New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28Si-enriched spheres were…
The new International System of Units may let us select an integer value for Avogadro's number. Some might prefer an integer that's divisible by 12, so that an integer number of $^{12}C$ atoms may be associated (to first order) with a…
Avogadro's number is a count of a definite number of things and, therefore, must be an integer and not a floating point number. Arguments are given herein that this integer should be precisely 2E79 - that is, N_o = 2E79 = 6.04 462 909 107…
The Pythagoras number of a sum of squares is the shortest length among its sums of squares representations. In many algebras, for example real polynomial algebras in two or more variables, there exists no upper bound on the Pythagoras…
We discuss the role of fundamental constants and measurement data for the Planck, Avogadro and Boltzmann constants and the elementary electric charge in connection with the planned transition to new definitions of four base SI units (the…
Analytical measurements of the 28Si crystal used for the determination of the Avogadro constant are essential to prevent biased results or under-estimated uncertainties. A review of the existing data confirms the high-purity of silicon with…
The latest determination of the Avogadro constant, carried out by counting the atoms in a pure silicon crystal highly enriched in 28Si, reached the target 2x10-8 relative uncertainty required for the redefinition of the kilogram based on…
We propose two experimental schemes to determine and so to realize the Avogadro constant $N\_{A}$ at the level of 10$^{-7}$ or better with a watt balance experiment and a cold atom experiment measuring $h/m(X)$ (where $h$ is the Planck…
About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely. The weakness of the gravitational…
We consider a recent proposal [1] to redefine the kilogram in terms of natural constants. In our opinion, the main objective of the redefinition should be to build such a version of the SI system in which the electric measurements are…
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…
The spacing of the \{220\} lattice planes of a $^{28}$Si crystal was measured by combined x-ray and optical interferometry to a $3.5\times 10^{-9}$ relative accuracy. The result is $d_{220}=(192014712.67 \pm 0.67)$ am, at 20.0 $^\circ$C and…
An additional value of the Avogadro constant was obtained by counting the atoms in isotopically enriched Si spheres. With respect to the previous determination, the spheres were etched and repolished to eliminate metal contaminations and to…
The measurement of the Avogadro constant by counting Si atoms is based on the assumption that Si balls of about 94 mm diameter have a perfect crystal structure up to the outermost atom layers. This not the case because of the surface…
The determination of the Avogadro constant plays a key role in the redefinition of the kilogram in terms of a fundamental constant. The present experiment makes use of a silicon single-crystal highly enriched in 28Si that must have a total…
The absolute position of the compact radio source at the dynamical center of the Galaxy, Sgr A$^*$, was known only to an accuracy of $0.2''$ in spite of its accurate location with respect to near-IR stellar sources to within 30…
In his seminal 1961 paper, Wirsing studied how well a given transcendental real number $\xi$ can be approximated by algebraic numbers $\alpha$ of degree at most $n$ for a given positive integer $n$, in terms of the so-called naive height…
We report on the precise measurement of the atomic mass of a single proton with a purpose-built Penning-trap system. With a precision of 32 parts-per-trillion our result not only improves on the current CODATA literature value by a factor…