The golden ratio is believed to underlie patterns in nature and beauty

Why patterns in art are so pleasing

Repeated visual cues like shapes or lines derive from the brain's innate compulsion to identify faces, places, bodies, and more. With repeated shapes, the brain seeks out resolution to the subtle variations between them. See examples in art and music.

The science of symmetry | The Royal Society

Nature is full of symmetries, from spiral galaxies to florets of broccoli. So why do complex creatures break the pattern?This short video discusses why symmetry came to dominate life on Earth, and how many complex life forms, such as humans, transitioned from radial to lateral symmetry.

Pareidolia: the cognitive bias of finding meaning in randomness

Many people equate "random" with "well-spaced," creating a cognitive bias that influences how people interpret events. This article explains how people tend to assume a generative force behind the patterns produced by randomness. This phenomenon, known as pareidolia, is seen in claims ranging from backward messages hidden in reversed audio recordings to tea leaf readings.

The most bizarre numbers in the universe

Even for math-y types, some numbers are incomprehensible. This article dives into several kinds of numbers more complicated than even irrational numbers with endless decimals like "pi" or Euler's number: Noncomputable numbers. Read the bizarre...

The 'Old Guitarist' challenged art's standards of beauty

For much of Western art history, the definition of “beauty” in art was dictated by academies rather than personal taste. Artists like Picasso challenged these standards with works considered “ugly” for discarding anatomical accuracy or linear perspective in favor of a feeling.

Apple's first logo was a portrait of Isaac Newton sitting under a tree

Before the minimalist image of an apple with a bite taken out of it, Apple's logo depicted the fruit dangling above the physicist, likely a nod to the anecdote about his epiphany regarding gravity.

The spiralling structure of the Guggenheim Museum in New York is itself a work of art

The Solomon R. Guggenheim Museum is a UNESCO World Heritage Site in Manhattan's Upper East Side. The contemporary art museum, known for its unique spiral structure, was Frank Lloyd Wright’s final work.

NASA designed the Golden Record using hydrogen to ensure it's universally readable

The Golden Record holds what is essentially a human "time capsule," featuring music, nature sounds, and greetings from around the world. NASA used the radiation period of hydrogen's simplest transition as a baseline to convey timing and structure. The first coded image is included on the cover as a test so aliens can check if they decoded it correctly.

View the Lorenz attractor, a graphical solution to chaotic equations that resembles a butterfly

The discovery of chaos theory came from Edward Lorenz's computer model of the atmosphere, which used three equations to quantify atmospheric circulation. However, the chaotic evolution of this system creates wandering figure-8-like shapes—some resembling butterfly wings—as it repeatedly attempts to settle on one of two values along unique trajectories.

The fast Fourier transform breaks down wave signals into discrete components

The algorithm was initially discovered by German mathematician Carl Friedrich Gauss in 1805, but his notes were not found until after his death. Today, FFTs form the basis for most compression software in media and are essential to technologies such as radar, sonar, and telecommunications.

Taxicab geometry defines displacement as the sum of vertical and horizontal distances

In this mathematical system, pi is valued at four, and circles aren't round—they appear as diamonds with corners instead. The system simplifies pixel distances in digital imaging and helps engineers with robot navigation and chip design.

Each design detail on the US $1 bill has significance

The eye in the triangle floating above the pyramid, for instance, is “the Eye of Providence watching over and ensuring the endurance of the structure of the American government.” This article details every design choice’s significance on the dollar—and a few conspiracies around these choices as well.

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

Romanticism was an 18th and 19th century creative movement

The movement emphasized the beauty of nature and human feeling. It was inspired by reactions against classical traditions, social injustices, technological change, and the philosophy of the Enlightenment. Although the movement spanned literature, visual art, music, poetry, and architecture, some of its most recognizable works are paintings.

Gustav Klimt featured a lot of gold leaf in his art

Austrian artist Gustav Klimt's most iconic image, "The Kiss," can be seen today printed on tapestries, t-shirts, mugs, and more. The painting comes from a decade in his career where gold held a prominent place. Klimt's family business of goldsmithing, in tandem with inspiration from Byzantine churches, coalesced in his obsession with gold.

People who feel connected to nature also report a higher well-being

Based on data collected from over 38,000 participants across 75 countries, spending time appreciating Earth's beauty appears to increase one's satisfaction with life. Whether it's a hike in the woods, a dip in the ocean, or time spent watching the sunset, the findings held true across a wide range of economic, cultural, and environmental contexts. The findings also indicate that connection to nature fosters experiences of being present and attentive, which are strongly linked to mental health.

The history and significance of rosemary

Rosemary is more than just an herb—it’s a powerful symbol intertwined with ancient Egypt, Christianity’s origins, Shakespeare, the culinary arts, and more. Native to the Mediterranean area, this plant has accompanied humanity for centuries, providing us with pleasant aroma, adornment, and even medicine. Explore this article for further insight into the significance of our long-standing relationship with rosemary.

The Koch snowflake has an infinite perimeter enclosing a finite area

Counterintuitively, although it would be impossible to build a fence along the edges of the shape because it would require an infinite amount of materials, this perimeter can be contained in a larger shape with a finite perimeter and limited area. This is equivalent to enclosing an infinitely long spiral that never reaches the center within a circle.

Chaos gardening involves scattering seeds without any planning

The trend is intended to produce colorful, dense gardens by mixing various seeds. While encouraging experimentation and lower stakes, the success of these gardens depends on choosing plants with similar needs and incorporating native, nectar-rich flowers.

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

Georgia O'Keeffe's flower paintings are often assumed to be sexual, though the artist claimed she was simply interested in highlighting the beauty of flowers that most people neglect

'All that is gold does not glitter, not all those who wander are lost; the old that is strong does not wither, deep roots are not reached by the frost.'

- "The Lord of the Rings" author JRR Tolkien (1892-1973)

Ancient Greek gymnasium: where philosophy met fitness

In ancient Greece, gymnasiums were not just places of physical training, but centers of intellectual life. This article explores the ways in which exercise, philosophy, and education were deeply intertwined, reflecting a cultural belief that physical fitness was essential for mental development.

Maya jade earflares were believed to open pathways to the divine

Carved from rare, hard-to-work jadeite, Maya earflares symbolized vitality and timelessness. Seen as living objects, they were believed to act as portals between the human and supernatural worlds, making finely crafted examples especially prized.

Many bitcoin enthusiasts have compared the cryptocurrency to digital gold

Gold is valued for its stability and reliability, serving as a hedge against inflation and economic uncertainty. Bitcoin shares both of these characteristics, but also provides near-instant liquidity and isn’t subject to government regulation.

The Five Pillars of Islam, explained through Islamic art at the Met

Fasting during Ramadan—known as sawm—is one of five foundational practices that define Muslim life. The Met uses art objects to illuminate the pillars to make the theology more tangible. Ramadan's fast is interwoven with this broader framework of prayer, charity, pilgrimage, and expressions of faith.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

Art theft is the third-largest source of criminal revenues worldwide, thanks in part to the subjective nature of valuing a work of art.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

Studies suggest when you sleep is as important as how much you get, and syncing with your circadian rhythms may lead to less fatigue and improved long-term health outcomes

All rainbows are 'raincircles' caused by water droplets separating white sunlight into a spectrum of colors, but Earth's surface blocks the bottom half of the circle from our line of sight.

See how each of the more than two million known species relates to each other—and to common ancestors—in this zoomable tree of life.

Salvador Dalí believed he was his own dead brother, who had died nine months before he was born

SpongeBob exemplifies Aristotle's philosophy for living well because he understands that happiness doesn't come from external factors like money, recognition, or power.

Learn more about the history of fireworks, which dates back to an accidental invention during an alchemist's quest for information about immortality.

The Brothers Grimm were lawyers before they were storytellers, and became interested in fairy tales as they began investigating how rules and customs had been passed down through cultures.

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'

The Nasdaq's 'Magnificent 7' companies are responsible for roughly 40% of the Nasdaq 100 index's gains, while the remaining 93 companies account for the other 60%.

Legendary architect Frank Lloyd Wright designed the SC Johnson headquarters in Wisconsin, aiming to make a cathedral-like workplace

Apeirophobia is an overwhelming fear of living forever, perhaps stemming from the brain's inability to conceptualize an infinite life.

Take a 3D tour of the Hajj, Islam's annual pilgrimage to Mecca, undertaken by more than 1.5 million Muslims each year.

Artificial coral reefs have been 3D printed from nontoxic, biodegradable terracotta clay, which coral polyps have used as a foundation for rebuilding marine ecosystems.

During the French Revolution, a botanist's letter asking about "dear Rhus" (poison ivy) was intercepted, leading authorities to suspect he was conspiring with the Russians.

Waves off the coast of Nazaré, Portugal, can reach over 100 feet and are caused by the area's deep underwater canyon geography

Power lines are dotted with large, brightly colored balls to improve the visibility of these thin wires to helicopters and small planes and help prevent potential crashes.

When you complete a CAPTCHA on a website to prove you are human, you may be unknowingly training algorithms for self-driving cars, whose systems require training data to help identify crosswalks, bicycles, and other outdoor objects.

Exploring the Larry Bird punch that almost changed March Madness