Offering A Showy Large Curled With Eyes At Base, On Matrix, Phacops Spine Trilobite. From Mt. Issimour,

A short note on how to interpret Fourier Series animations

When one searches for Fourier series animations online, these amazing gifs are what they stumble upon.

They are absolutely remarkable to look at. But what are the circles actually doing here?

Vector Addition

Your objective is to represent a square wave by combining many sine waves. As you know, the trajectory traced by a particle moving along a circle is a sinusoid:

This kind of looks like a square wave but we can do better by adding another harmonic.

We note that the position of the particle in the two harmonics can be represented as a vector that constantly changes with time like so:

And being vector quantities, instead of representing them separately, we can add them by the rules of vector addition and represent them a single entity i.e:

                                                  Source

The trajectory traced by the resultant of these vectors gives us our waveform. 

And as promised by the Fourier series, adding in more and more harmonics reduces the error in the waveform obtained.

        Have a good one!

**More amazing Fourier series gifs can be found here.

Stanley Kubrick | 2001: A Space Odyssey

lymeregisfossils Thursday lunchtime on the Jurassic 🦕Coast🌊 ! The “ammonite graveyard” -a limestone bed literally packed full of 190 million year old fossil ammonites!

Breakfast far above the clouds, Pokut, Turkey

WHAT A JERK

The Bortle Scale and Light Pollution

The Bortle Scale is used by astronomers to rate the darkness of our skies. It ranges from 1 (darkest) to 9 (brightest). For most of us, our daily lives are spent beneath a radiance level of between 5 and 8 and rarely venture into areas ranked 3 or darker- and what a shame that is.

Light pollution, while a testament to our technological advances, has blanketed our view of the universe and decoupled our relationship with the cosmos. For the millions of people living in areas where less than 20 stars can be seen in the night sky, it is practically impossible to imagine a natural sky blanketed with upwards of 2,500 stars backed by great ribbons of billions of stars which can be found in our Galaxy: The Milky Way.

What are the effects of light pollution?

Continuar lendo

Sittin at the desk

Palaeovespa florissantia This exceptionally preserved 34 million year old wasp was found and identified in what is today Florissant Fossil Beds National Monument in Colorado. This species is a member of the same family of life that today also contains hornets and yellow jackets. The incredible preservation of this insect is one example of the fossils found in Eocene aged lake sediments in this part of Colorado (https://tmblr.co/Zyv2Js296djPx). The area was heavily picked over for fossils prior to establishment of the National Monument and there were even attempts to establish housing developments on the site before it received protection. Today this insect is pictured in the logo of this monument and shots of it can be found around the parking lots at the site. -JBB Image credit: NPS http://bit.ly/2nYZwga References: https://www.revolvy.com/page/Vespinae http://bit.ly/2N9jn7k