Parallel lines are defined as lines that lie in the same plane and never intersect, no matter how far they are extended. A key characteristic of parallel lines is that they have the same slope.

Motivated by electrodynamics we discuss a derivation of the Stokes theorem which is based on the variations of the fluxes and line integrals of vector fields. We show how this procedure can be ...

This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

Horizontal lines run left to right, parallel to the horizon, with slope 0 and equation y = k. Vertical lines run top to bottom, perpendicular to the horizon, with undefined slope and equation x = k.

Abstract: This paper faces a challenge in power education: how to teach the students the impact of different transmission lines on the power system at power frequency. More specifically, the paper ...

Cluster algebras and scattering diagrams appear in diverse areas of mathematics and physics including total positivity, Seiberg duality, statistical physics models, noncommutative geometry, tropical ...

The Dungey cycle is considered from the formation of a magnetic barrier and necessary for dayside reconnection conditions till the electric field generation around the Birkeland current loop and ...

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The Kármán line, about 62 miles (100 km) high, marks where aircraft can no longer fly without special propulsion. Above the Kármán line, aerodynamic lift is insufficient; spacecraft need different ...

You might be surprised to learn that you can’t comb the hairs flat on a coconut without creating a cowlick. Perhaps even more surprising, this silly claim with an even sillier name, the “hairy ball ...

Abstract: This paper presents the application of Belevitch theorem for pole-zero analysis of microwave filters synthesized with transmission lines and lumped elements. The scattering (S) matrix ...