Figuring out how to get a sofa around a corner has been a math problem since 1966

How the number 15 solved a longstanding math challenge

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer—only 15. While...

It took 70 years for computer scientists to determine how to cut a cake fairly

The cake-cutting problem explores how to divide something fairly, which is not solely about cutting evenly-sized pieces. A protocol that accounted for personal preferences (e.g., a corner piece) between just three people took 16 years to develop.

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.

The architect who made the most of a tiny New York apartment

This short documentary explores the 350-square-foot apartment of Ben Riskin, a New York resident looking to make the most of his new home through hidden storage and ingenious design.

How a bicycle inspired an iconic armchair

The Wassily chair, also known as the Model B3, is one of the most recognizable and mass-produced pieces of modernist furniture. It was designed by Marcel Breuer—a Bauhaus student in the early '20s who went on to lead the school's carpentry workshop—who was inspired by the modular tubes and simple construction of a bicycle he'd purchased.

Watch every 'Simpsons' couch gag

One of the most recognizable elements of "The Simpsons" opening sequence is the "couch gag," a visual joke (featuring the family sitting on their living room couch) that often changes. This collection compiles every one of them through Season 34.

Within topology, time can be modeled as restarting after reaching its 'edge'

A manifold is any space that appears flat when zoomed in close enough, even if it is globally curved. Some of these structures can be curved to connect back on themselves, much like bending a line into a circle. This property can be mathematically established in a four-dimensional manifold by allowing time to loop back on itself.

Scientists now know why wombats poop cubes

For years, scientists have been wondering why wombat poop is cube-shaped (yes, really). Now, they say they have got to the bottom of the mystery.

The world's largest restaurant is the size of 10 football fields

The Bawabet Dimashq Restaurant in Damascus, Syria, has held the Guinness World Record for largest restaurant since 2008. It can seat 6,014 guests and employs nearly 1,800 people, who serve up an eclectic menu of Middle Eastern Indian, Arab, Iranian, Syrian, and Chinese dishes.

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.

Explore a gallery of O'Neill cylinder space settlements

The structures consist of a pair of cylinders with a total enclosed land area of 500 square miles and can house several million people. Each is approximately 20 miles long, 4 miles in diameter, and contains three mirrors that open and close to form a day-night cycle inside.

The next generation of gravitational wave detectors may include a triangular design

The Einstein Telescope will use three pairs of underground detectors—each with arms separated by 60 degrees—arranged in an equilateral triangle. The European observatory will work alongside the Cosmic Explorer, a pair of new US detectors, to provide an eightfold increase in sensitivity over LIGO and extend the current detection frequency range.

Wikipedia's puzzle globe logo was developed by a 17-year-old

In 2003, the site held a contest for its users to submit designs for a new logo. Paul Stansifer submitted the winning design, which used the incomplete puzzle as a symbol for the encyclopedia being a work in progress. Symbols and letters would later replace text within Stansifer's colorful design.

As of 2025, the Factory of the Future 1.0 is the world's largest 3D printer

Housed at the University of Maine, the machine incorporates AI and can utilize bio-based materials to construct homes exceeding 3,000 square feet in size. Homes made from these materials are fully recyclable, as their components can be deconstructed, ground up, and reused as raw materials for printing.

The Oval Office was completed in 1909

Completed during William Howard Taft's presidency, the Oval Office was designed as part of an expansion of the West Wing. President Franklin D. Roosevelt redesigned the room and moved it to the southeast corner of the West Wing in 1934.

Are there any planets in the universe that aren’t round?

We think of all planets as spheres, but do they have to be spheres? To be classified as a planet, an object has to be sufficiently massive to reach a spherical shape through gravity. However, this doesn't mean they're perfectly round; for example, Earth has a slight equatorial bulge caused by centrifugal force from its rotation. Other observed planets feature tear-shaped formations while theorists posit donut-shaped planets. Read more here.

Corkscrew roller coasters feature tracks that twist 360 degrees around their axis

Thanks to the incorporation of steel, rides have gotten increasingly versatile, daring, and smooth, performing loops and turns that are much more difficult to safely achieve with wood.

Sudoku was originally called 'Number Place'

While there are earlier variations on the game, the modern version appeared in 1979, though it was then called "Number Place." The game was slightly altered and renamed in Japan.

The term 'gerrymander' dates back to a 1812 Boston dinner party

The term "gerrymandering" arose when Massachusetts Governor Elbridge Gerry approved a state senate map with a district so contorted it resembled a salamander. Critics dubbed it the "Gerry-mander," cementing the term for partisan map manipulation.

What is the 240 paychecks retirement rule?

Many people think about the large sum of money they'll require to retire comfortably. It can be intimidating. The 240 retirement method breaks that thinking down into paychecks. Specifically, the framework argues that the average retiree will need 240 paychecks to retire. Learn more here.

Jim Simons, mathematician turned government codebreaker turned trader, revolutionized quantitative investing

The late Jim Simons is remembered as one of the most successful (and profitable) hedge fund managers of all time. He went from physically gathering microfilm on commodities pricing decades ago to overseeing a firm that led Wall Street in daily trading volume.

How the ancients calculated Earth's size correctly

Watch this seven-minute video to hear Carl Sagan explain how ancient Greek polymath Eratosthenes correctly calculated the size of the Earth in the third century BCE. At some point, Eratosthenes noticed a discrepancy in the length of shadows cast in different cities during the summer solstice. This observation grew into a simple experiment that enabled Eratosthenes, the head librarian at the Library of Alexandria, to calculate the Earth's size precisely.

Google began as a Stanford University dorm room project

Launched in 1998, Google revolutionized search engines with its clean design and PageRank algorithm. As of 2025, Google has about 90% of the search market share but faces new challenges from AI-powered competitors and regulatory scrutiny.

The perfectly rolled burrito depends on the tortilla

Experts recommend warming a tortilla before wrapping it around the filling. Once warm, you should distribute the ingredients evenly on the back half of the tortilla for a uniform shape.

'Jeopardy!' super fans use a specific method to calculate a player's score

In its many decades on the air, “Jeopardy!” has developed a fervent fanbase that likes to play along at home. The Coryat score was developed by Karl Coryat, who appeared on the show in 1996. The equation ignores forced responses on Daily Doubles and Final Jeopardy! Correct responses for Daily Doubles are scored as their natural value.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

Massive 3D printers have been used to build homes by stacking layers of 'concrete toothpaste,' a fire-resistant material that effectively insulates against outside noise.

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

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

Explore an interactive map built from more than 100,000 survey responses on where people find joy in their lives

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.

Search a massive database of over 4 decades of clues from the TV quiz show 'Jeopardy!'

Explore fun facts from the USPS, including unique post office buildings, a stamp that traveled past Pluto, and more.

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.

In 1963, a basement renovation in Turkey revealed a passageway to a hidden, multilevel underground city that once housed as many as 20,000 people

Larger animals like giraffes, elephants, and blue whales have developed a unique defense against cancer, a phenomenon known as Peto's Paradox

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.

To reduce wrinkles in clothing, research recommends gentle wash cycles with more water and tumble drying with smaller loads and longer times.

Calculate how much of your tax dollars go to each federal program based on your income, filing status, and number of children

Sony set the standard for cylinder-shaped batteries when it repurposed manufacturing equipment used to make rolls of magnetic recording tape.

Quincy Jones' 'Big Band Bossa Nova' helped introduce bossa nova—a jazz-influenced Brazilian genre—to the US

US housing costs have risen by roughly 175% between 1991 and 2026—but a growing number of Gen Zers are becoming homeowners anyway. In 2025, 4% of homebuyers were Gen Z, up from 3% the year before.

Watch this video that uses Lego bricks to explain how venture capital works.

A Yale student wrote a profound essay about the consulting industry's influence on elite college students that was published in a book of her writing after she died in a post-graduation car accident.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

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

Hurricanes, which rely on air consistently spinning in the same direction, cannot cross the equator because air curves in opposite directions north and south of it.

Domino's Pizza's 30-minute delivery guarantee was responsible for the chain's 1980s surge, but it was discontinued after the company was found liable for delivery driver accidents.

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

In 1945, Surrealist artist Salvador Dalí and legendary animator Walt Disney began collaborating on a short film that was not completed until 2003, years after both men had died.