Related papers: Hemaka's constant
There is little known about the methods used by the ancient Babylonians and Egyptians to arrive at their recorded estimates of the value of Pi. A surprisingly accurate estimate of Pi was recently revealed coded within a verse in the book of…
The ratio of the circumference, C, of a circle to its diameter, D, is a constant number denoted by $\pi$ and is independent of the size of the circle. It is known that $\pi$ is an irrational number and therefore cannot be expressed as a…
This study reconstructs the origin of a constant, here called $\Xi$ (Xi), as a primary scaling factor in Old Babylonian mathematics and astronomy. $\Xi$ arises from the practical necessity of precise measurements on the sky or a circle,…
The study of the mathematics and geometry of ancient civilizations is a task which seems to be very difficult or even impossible to fulfil, if few written documents, or none at all, had survived from the past. However, besides the direct…
How were surfaces evaluated before the invention of the sexagesimal place value notation in Mesopotamia? This chapter examines a group of five tablets containing tables for surfaces of squares and rectangles dated to the Early Dynastic…
I have recently proposed that an object, found in an Egyptian tomb and exposed at the Egyptian Museum of Torino, could be a protractor. The tomb was that of architect Kha, supervisor at Deir El-Medina during the 18th Dynasty, and his wife…
We answer the question: who first proved that $C/d$ is a constant? We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the circle and that the circumference constant…
In his treatise addressed to Dositheus of Pelusium, Archimedes of Syracuse obtained the result of which he was the most proud: a sphere has two-thirds the volume of its circumscribing cylinder. At his request a sculpted sphere and cylinder…
We will discuss about a possible method of using the cubit rod by the architects and the surveyors of Ancient Egypt to measure and draw lengths, comparing it with the other interpretations present in Literature. Instead of the modern…
We study the evolution of the configuration entropy for different combinations of $\Omega_{m0}$ and $\Omega_{\Lambda0}$ in the flat $\Lambda$CDM universe and find that the cosmological constant plays a decisive role in controlling the…
Ratios and coefficients are used to simplify calculations. For geometric usage these values also called function values. Like in Egypt also in Babylon such a value system can be shown. The reconstructed calculation sequence, of the Plimpton…
This talk describes an analytic calculation of the position of the first accoustic peak as a function of the matter density and the cosmological constant (work with Y.J. Ng and R. Rohm), agreeing with independent numerical studies. There is…
We present the first observational confirmation for an extended circumstellar dust disk around epsilon Eri. The observations were obtained with the bolometer array SIMBA at the 15 m radio telescope SEST in Chile and measure the dust…
The Great Pyramids of Egypt hide mathematic information unknown up to date. The measurements of the three Great Pyramids of Egypt at Giza show that Egyptians knew how to calculate the circumference, the volume and the area of the sphere…
Studies of ancient bronze artifacts can be useful in understanding the progression of human knowledge of mathematics and geometry. Here I discuss the decoration composed by several circles and spirals of the Langstrup belt disk, an artifact…
In this paper the smallest or optimal dimensions of a Halbach cylinder of a finite length for a given sample volume and desired flux density are determined using numerical modeling and parameter variation. A sample volume that is centered…
Egyptologists and historians of mathematics around 1930 did an admirable job in showing that problem 14 of the newly discovered Moscow Papyrus from around 1850 BCE amounts to a general and exact calculation of the volume of a truncated…
A series of peculiar, visual alignments between the pyramids of the pharaohs of the 4, 5 and 6 Egyptian dynasties exists. These alignments governed from the very beginning the planning of the funerary monuments of successive kings and, in…
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance…
In this paper we state a one-to-one connection between the maximal ratio of the circumradius and the diameter of a body (the Jung constant) in an arbitrary Minkowski space and the maximal Minkowski asymmetry of the complete bodies within…