John Edmark is an artist and professor at Stanford University who has used the Golden Angle to sculpt spirals. The Golden Angle is derived from the Golden Ratio: it is the smaller of the two angles created by dividing the circumference of a circle according to the golden ratio and comes out to be around 137.5°.

Today I thought I’d share a video that I came across the other day. Hope you enjoy!

“Bacteria and viruses hitch a ride inside droplets of all kinds—sneezes, raindrops, toilet splatter. By reviewing footage of different types of drops, applied mathematician Lydia Bourouiba records and measures where they disperse in order to better understand how diseases spread. Watch how Bourouiba designs tests—some inescapably humorous and awkward—to study infectious disease transmission.”

Today I wanted to share with you a video which I came across the other day on the Map of Mathematics.

Although many people view maths as synonymous with pain, boredom or frustration, one must appreciate its diversity and vast implications on other subjects; you may not have the background to see beauty in a particular equation, but virtually anyone can appreciate the amazing advancements humans have made from basic counting to creating full-on artificial intelligence.

“While an artistic temperament is often considered the exact opposite of the kind of personality that loves complicated equations, pure mathematicians are really just a bunch of lunatics endlessly working with abstraction and beauty.“

– Rhett Jones

In the video below, Dominic Walliman takes viewers through the major fields of math starting at the beginning and shows us how they inform and relate to each other. Of course many details have been left out, as to properly connect the various disciplines of math we would need a 3D web! Also, in reality, “the study of math’s foundations has yet to discover a complete and consistent set of axioms.“

The Banach-Tarski Paradox is a theorem in geometry which states that:

“It is possible to decompose a ball into five pieces which can be reassembled by rigid motions to form two balls of the same size as the original.”

It was first stated in 1924, and is called a paradox as it contradicts basic geometric intuition.

An alternate version of this theorem tells us that:

“It is possible to take a solid ball the size of a pea, and by cutting it into a finite number of pieces, reassemble it to form a solid ball the size of the sun.”

Below is an awesome video explaining how this paradox works:

Numberphile has recently posted a video on Space-Filling Curves, a topic I made a post on a few weeks ago. I thought I would share this video as it would be a nice complement to that post!

Ernst Chladni was a German physicist who is sometimes labelled as the ‘father of acoustics‘. His work in this area includes research on vibrating plates and the calculation of the speed of sound for different gases.

One of Chladni’s greatest achievements was his invention of a technique to show the various methods of vibration of a rigid surface, such as a plate, which he detailed in his book Entdeckungen über die Theorie des Klanges (“Discoveries in the Theory of Sound”) in 1787. His technique entailed:

“drawing a bow over a piece of metal whose surface was lightly covered with sand. The plate was bowed until it reached resonance, when the vibration causes the sand to move and concentrate along the nodal lines where the surface is still, outlining the nodal lines.”

The patterns that emerge are beautiful and are now known as Chladni figures, although Chladni was building on experiments and observations by Robert Hooke in 1680 on vibrating glass plates.

Chladni also created a formula that successfully predicted the patterns found on vibrating circular plates.

Chladni’s discovery was extremely important as it inspired many of the acoustic researchers who later extended his work.

Once these patterns were well understood, they began to have many practical uses, for example violin makers use “Chladni figures to provide feedback as they shape the critical front and back plates of the instrument’s resonance box“.

I thought I’d share a fun video of a math parody of one of the hits of one of my favourite musicals: Hamilton.

This parody is centred around the great Irish mathematician and physicist William Rowan Hamilton, who was featured in my post about vectors a few weeks ago.

The lyrics discuss his love life, alcoholism, study of optics and his creation of quaternions.

It’s fantastically done and I’d like to applaud these scientists for their awesome creativity!