Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1203.4103

Number pi from the decoration of the Langstrup plate

Amelia Carolina Sparavigna
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 of the Bronze Age found in Denmark. I am showing by measurements of diameters and distances of spirals, that the artist who made the decoration knew some approximations by rational numbers of the number pi, the dimensionless physical quantity representing the ratio of circumference to diameter.

Explore related subjects

physics.pop-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Amelia Carolina Sparavigna. 2012-03-19. Number pi from the decoration of the Langstrup plate. https://arxiv.org/abs/1203.4103

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Mass in the Light of Special Relativity

The text analyzes the concept of mass within Special Relativity, initially deconstructing the interpretation of Einstein's equation ($\varepsilon_\circ = m c^2$) as a principle of equivalence. Based on the adoption of the conservation laws of momentum and energy, the non-additivity of mass in composite systems is established. While in atomic and nuclear systems the total mass is less than the sum of its constituents, in the subnuclear domain the opposite occurs: the positive potential energy of confinement of quarks causes the mass of a hadron to be greater than the sum of the masses of its quarks; in the case of nucleons, it is much greater. It is concluded, then, that the mass of baryonic matter in the observable Universe comes, for the most part, from the energy associated with strong interactions.

physics.pop-ph↗
arXiv2026

Understanding Quaternions and the Dirac Belt Trick

The Dirac belt trick is often employed in physics classrooms to show that a $2π$ rotation is not topologically equivalent to the absence of rotation whereas a $4π$ rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors has been achieved, or if the trick is just an amusing analogy. The goal of this paper is to demystify the belt trick and to show that it implies an underlying \emph{four-dimensional} parameter space for rotations that is simply connected. An investigation into the geometry of this four-dimensional space leads directly to the system of quaternions, and to an interpretation of three-dimensional vectors as the generators of rotations in this larger four-dimensional world. The paper also shows why quaternions are the natural extension of complex numbers to four dimensions. The level of the paper is suitable for undergraduate students of physics.

physics.pop-ph↗
arXiv2026

Project Setu: 3D Multi-Physics Design and Scaled Structural Analysis for a Relativistic Lightsail Architecture

Deep-space exploration beyond the solar system requires eliminating chemical propellant mass penalties to achieve relativistic flight velocities (0.166c at 180 s, reaching the mission target of 0.20c at 227 s). This study presents a 3D multi-physics numerical framework for a 4.0-meter circular lightsail propelled by a 100 GW ground laser array, coupling 3D Maxwell FDTD wave optics, non-linear membrane mechanics, and Stefan-Boltzmann thermal radiation in ANSYS Mechanical APDL and Ansys Lumerical. A four-level grid convergence study establishes numerical independence with an ASME GCI_21 of 0.13%, resolving peak membrane stresses of 530.88 MPa with a 3.77x safety factor against stoichiometric Si3N4 tensile failure. With optical absorption constrained to 10 ppm (A = 1.0 x 10^-5), the steady-state core temperature stabilizes at 923.02 K (0.44% deviation from radiation theory), maintaining a +1,247 K margin below sublimation, while fundamental drumhead modal resonance (7.92 Hz) provides a 7.92x safety buffer against laser jitter. The electrodynamic radiation pressure formulation is cross-verified against published flight telemetry from JAXA IKAROS and NASA LightSail 2 within 0.12% and 2.13%, confirming classical momentum transfer modeling across solar and beamed propulsion regimes.

physics.pop-ph↗