Category: Nature

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Walking on Water—No Miracle Needed!

Paper wasps (Polyistes dominula) stand on the water’s surface while drinking. The ‘surface tension‘ of the water, a property that causes water molecules to stick together, acts like an elastic sheet, supporting the wasp’s weight. The wasp’s six legs create depressions in the surface, forming lens-like curvatures that cast tiny shadows beneath the water. Surface tension is crucial for many organisms, as it creates a habitat for various life forms on the water’s surface.

surface-tension-formula

In this formula, surface tension (γ) represents the force across an imaginary line divided by twice the length of that line. The factor of 2 is essential because, when splitting the surface of a bubble, we’re actually pulling apart molecules on two surfaces—the inner and the outer.

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The Doppler Effect: A Mathematical Symphony

Imagine a siren on a fire truck…
· When the truck is approaching you: The siren’s sound waves are compressed, making it sound higher pitched. It’s like the truck is “pushing” the waves together.
· When the truck is moving away from you: The siren’s sound waves are stretched out, making it sound lower pitched. It’s like the truck is “pulling” the waves apart.
This is the Doppler effect: the change in pitch of a sound wave due to the relative motion between the source of the sound and the observer.
The same concept applies to light waves, with objects moving toward us appearing bluer and those moving away appearing redder.

⇨ Further reading.

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Logarithmic and Fibonacci Spirals in Plant Phyllotaxis

Nature, particularly in plants, features logarithmic and Fibonacci spirals, exemplifying the elegance of natural design and the rhythmic dance of life, encompassing symmetry and other intriguing mathematical phenomena, including recursive functions.

Spiral patterns in plants emerge from their repetitive growth, where each turn closely mirrors the previous one with scaling or rotational adjustments. This growth process, common in nature and known as phyllotaxis, utilizes recursive functions, which can generate logarithmic and Fibonacci spiral patterns.

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The Fascinating World of Runic Calendars

The Runic calendar, also referred to as a Rune almanac, served as a perpetual timekeeping tool throughout Northern Europe until the 19th century. Structured with lines of symbols, it marked significant astronomical events and celebrations, including solstices, equinoxes, and Christian holidays. These symbols were often etched onto parchment or carved into various materials such as wood, bone, or horn.

One of the most esteemed examples of these calendars is Worm’s Norwegian runic calendar from 1643, renowned for its bone craftsmanship. Danish Antiquarian Ole Worm featured it in his book “Fasti Danici, universam tempora computandi rationem antiquitus in Dania et vicinis regionibus observatam libris tribus exhibentes.” Although he extensively detailed the winter months in his work, he omitted details regarding the summer season. Fortunately, supplementary insights are provided through ‘runstavs’ and ‘primstavs.’ ‘Runstavs’ served as runic sticks used in divination practices, while ‘primstavs’ were Norwegian wooden calendar sticks primarily employed for timekeeping and weather prediction.

runic calendar


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Beyond 65 digits, π serves no practical purpose

For spatial engineers’ highest accuracy calculations, used in interplanetary navigation, 3.141592653589793 is more than sufficient. Let’s understand why more decimals aren’t needed.

Consider these examples:

• Voyager 1, the farthest spacecraft from Earth, is about 14.7 billion miles away. Using π rounded to the 15th decimal, the circumference of a circle with a radius of 30 billion miles would be off by less than half an inch.

• Earth’s circumference is roughly 24,900 miles. The discrepancy using limited π would be smaller than the size of a molecule, over 30,000 times thinner than a hair.

• The radius of the universe is about 46 billion light years. To calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom, only 37 decimal places are necessary.

• With just 65 decimal places, we could determine the size of the observable universe within a Planck length, the shortest measurable distance.

While π’s digits are endless, for microscopic, macroscopic or cosmic endeavors, very few are necessary.

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Illusion vs Reality

“Illusion, a derivative of reality, and vice versa.” – GS

For a little backstory… one day, a follower threw me a curveball: ‘What separates illusion from reality?’ I countered with a snap response: ‘What separates acceleration from speed?’

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Wandering Eye

The entire sea urchin functions as a massive compound eye because each of its spines conceals tube feet with light-sensitive cells at their bases. Essentially, a sea urchin is one large, moving, spine-covered eye. While its vision might not astonish an eye doctor, for an animal devoid of actual eyes, it’s rather impressive!

A representation of the computational model of the ‘spherical’ vision of the sea urchin.

For further details, you can read more here.

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Visual Maths


Mathematical objects like spirals and fractals can serve as art. Their deceptively simple nature adds an extra allure to this artistic expression.

Explore the realm of Visual Mathematics, a distinctive fusion of Art and Math. Delve into intricate diagrams, tables, and visually captivating pieces that provide a delightful experience for both the eye and the mind. Visit our online gallery for prints, posters, and t-shirts showcasing beautiful math art.

Math and Art
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The Golden Ratio is implemented in circles, serving as a mathematical ratio for generating aesthetically pleasing designs. Given its prevalence in nature, the natural appearance of outcomes is unsurprising.

Golden ratio with circles
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The Golden Diamond presents an asymptotic monomorphic dissection of the equilateral triangle. Each tile follows proportions aligned with the golden ratio in relation to the outer triangle.

Golden ratio with equilateral triangles
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Golden Spiral created using equilateral triangles. The Padovan spiral follows a recursive sequence akin to the Fibonacci sequence.

Padovan spiral
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