QR codes can be scanned from any angle because of the squares in their corners, which communicate the code's size and orientation.

Although circular pies have sometimes appeared in circular boxes, they usually travel in square, cardboard boxes. That's because the cardboard industry manufactures them with edges so they can be made in one piece and be easily stacked.

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.

Magnetic strips store unchanging data that is easily cloned, but microchips act as miniature computers that encrypt sensitive data. They also resist fraud by creating data unique to each transaction, preventing duplication.

The process of determining the order of nitrogenous bases in DNA involves first cutting the DNA into fragments, which are duplicated multiple times using bacteria. Fluorescently labeled terminator bases are added to fragments, which are sorted by length and read via laser to reconstruct the sequence.

Capital One estimates that 169.2 million Americans redeemed digital coupons in 2025. The bank compiled many different coupon statistics on how both shoppers and businesses used coupons last year, most of which reveal the increasing dominance of digital coupons over physical ones.

Rather than directly energizing neon atoms, electrical discharge at lower, more practical power levels can excite helium atoms to energy levels nearly equal to those in neon atoms. Within a helium-neon laser, these gases are present in a 10-to-1 ratio, enabling helium to efficiently transfer energy to neon, which is then discharged as red light.

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.

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

By translating binary code into the base-pair code found in genetic sequences, researchers in China are storing digital data on DNA-coated tapes for compact, durable, and energy-efficient storage. The tapes use a blend of polyester and nylon with barcode patterns for data addressing.

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

Traditional quantum computers are incredibly fragile, with encoded information easily disrupted and requiring significant error correction systems. Microsoft’s approach involves storing data on a surface, which is more stable, but involves an elusive particle first theorized in 1938.

The pits are dips in the LaserDisc, CD, DVD, or Blu-ray surface that do not reflect the laser from the optical drive back to the photoelectric cell, resulting in a coded zero. Lands are reflective plateaus on the surface that code for a one.

Its ability to bend around obstacles and reflect off the ionosphere—an electrified layer of Earth's upper atmosphere—allows this type of light to travel long distances without damaging living things due to its low energy. MRI scanners, WiFi, and Bluetooth technologies are also applications of this form of light.

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...

In 1994, Peter Shor introduced an algorithm that showed a quantum computer could efficiently factor the product of two very large prime numbers, undermining the mathematics that makes RSA so secure. While using larger keys can delay the decryption time of quantum computers, this solution increases the time it takes to encrypt data, which may become impractical.

In the 1800s, the postcard was a relatively new phenomenon, as was the post office. In the burgeoning system, recipients of mail had to sometimes pay prohibitively costly fees to receive it. So to get around the fees, a system of placing stamps on the envelopes in specific ways to communicate—a simple yes or no—was devised by clever mailers and expanded and codified by postcard companies into guides. Learn about the fascinating system here.

Russian mathematician Georg Cantor demonstrated that certain sets of numbers (e.g., the natural numbers) form countable infinities, while others cannot be counted (e.g., the real numbers) and are therefore uncountable, representing larger versions of infinity. Through the axiom of choice, German mathematician Ernst Zermelo proved this concept of ordering infinities.

From the Greek word for "hidden writing," cryptography in Ancient Greece took the form of batons around which a long strip of leather or parchment was wrapped, after which messages were written. Recipients needed a scytale of the correct width to encircle received ribbons and reveal the message. Members of the Navajo Nation created a code that remained unbroken throughout its use in World War II.

Property boundaries, such as anti-climb fencing, overlapping cameras, vehicle crash barriers, and circulating patrols, are coupled with lobby iris scans and ID and badge checks. The security operations center monitors individuals throughout their visit, including the less than 1% of Google users who ever receive permission to visit the data center floor.

A sofa with the largest possible area that can make a 90-degree turn is known as Gerver's sofa, named after the mathematician who determined the shape in 1992. In 2025, a 119-page paper provided the proof confirming this shape.

That’s compared to 28% for physical coupons, representing the year the balance of power shifted in digital’s favor. The COVID-19 pandemic era’s lockdowns increased online shopping, which accelerated digital coupon adoption.

The country's eye-catching sewer covers were a form of brand rehabilitation, intended to change people's perceptions of the sewer. Additionally, they're easy to see at night, making firefighters' nighttime duties a bit easier.

There are four bases—adenine, thymine, cytosine, and guanine—which keep the two strands of DNA connected via chemical bonds between them. Connections between thymine and adenine require two hydrogen bonds, while those between cytosine and guanine need three hydrogen bonds. These differences in bond number prevent non-complementary pairings.

Resulting from a mutation on the X chromosome, the rare genetic condition causes individuals to possess an additional type of photoreceptor cell, typically sensitive to the orange range, located between the standard red and green cones. This enables the perception of approximately 100 million colors.

Isometric NYC is a zoomable pixel-art map that renders the city in game-style perspective (think SimCity), helpfully clarifying the dense geography and architecture. The makers built the project tile-by-tile using satellite data and generative AI. Zoom into building-level views or out to see all five boroughs.

Various geometric models, including Newton's color circle of hue and saturation and the horseshoe-shaped XYZ space for mixing colors via vector mathematics, have been proposed to describe colors accurately. However, these models do not encapsulate the variety of psychological effects that cause perceived colors to differ from mathematical representations.

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.