Articles by Greg Bernhardt

The concept of quantum superposition (or superposition for short) is very counterintuitive, as Schr##\ddot{\text{o}}##dinger noted in 1935 writing...

[caption id="" align="alignright" width="269"] Figure 1: A slinky, the subject of the slinky drop experiment. Attribution: Roger McLassus. CC...

Introduction [caption id="attachment_45195" align="alignright" width="238"] A double-double (AM-2) Atwood machine.[/caption] The figure on the...

Preamble The classical mathematician practically by instinct views the continuous process as the "real" process, and the discrete process as an...

A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs: What if it...

Introduction This elaborates some of the claims in my insights article on digital audio. The Sinc Function The first link in my insights...

Introduction First, we need some background in Digital Signals. This can be mathematically quite advanced, but since I would...

Introduction Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th...

Abstract I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the...

Introduction In a previous article on measuring battery internal resistance, a simple technique for low-resistance measurement was outlined. In...

Abstract "Mathematics is the native language of nature." is a phrase that is often used when it comes to explaining why mathematics is all around...

Introduction I am convinced students learn Calculus far too late.   In my view, there has never been a good reason for this. In the US, they...

Introduction When doing mathematics,  we usually take for granted what natural numbers, integers, and rationals are. They are pretty intuitive. ...

Introduction The applicability of Newton's second law in the oft-quoted "general form"...

Abstract Richard Pierce describes the intention of his book [2] about associative algebras as his attempt to prove that there is algebra after...