# Random Articles

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# Tweel – Airless Wheel

The **Tweel** (a portmanteau of *tire* and *wheel*) is an airless tire design developed by the French tire company Michelin. Its significant advantage over pneumatic tires is that the Tweel does not use a bladder full of compressed air, and therefore cannot burst, leak pressure, or become flat. Instead, the Tweel's hub is connected to the rim via flexible polyurethane spokes which fulfil the shock-absorbing role provided by the compressed air in a traditional tire.

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- "Tweel – Airless Wheel" | 2015-02-24 | 40 Upvotes 16 Comments

# Coulomb explosion

**Coulombic explosions** are a mechanism for transforming energy in intense electromagnetic fields into atomic motion and are thus useful for controlled destruction of relatively robust molecules. The explosions are a prominent technique in laser-based machining, and appear naturally in certain high-energy reactions.

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- "Coulomb explosion" | 2015-03-09 | 94 Upvotes 4 Comments

# Ludus Latrunculorum

**Ludus latrunculorum**, **latrunculi**, or simply **latrones** (“the game of brigands”, from *latrunculus*, diminutive of *latro*, mercenary or highwayman) was a two-player strategy board game played throughout the Roman Empire. It is said to resemble chess or draughts, but is generally accepted to be a game of military tactics. Because of the scarcity of sources, reconstruction of the game's rules and basic structure is difficult, and therefore there are multiple interpretations of the available evidence.

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- "Ludus Latrunculorum" | 2021-04-05 | 61 Upvotes 8 Comments

# Tarski's high school algebra problem

In mathematical logic, **Tarski's high school algebra problem** was a question posed by Alfred Tarski. It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics. The question was solved in 1980 by Alex Wilkie, who showed that such unprovable identities do exist.

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- "Tarski's high school algebra problem" | 2013-03-07 | 76 Upvotes 18 Comments

# List of Unexplained Sounds

The following is a list of unidentified, or formerly unidentified, sounds. All of the sound files in this article have been sped up by at least a factor of 16 to increase intelligibility by condensing them and raising the frequency from infrasound to a more audible and reproducible range.

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- "List of Unexplained Sounds" | 2012-06-17 | 280 Upvotes 75 Comments

# Time formatting and storage bugs

In computer science, **time formatting and storage bugs** are a class of software bugs which may cause time and date calculation or display to be improperly handled. These are most commonly manifestations of arithmetic overflow, but can also be the result of other issues. The most well-known consequence of bugs of this type is the Y2K problem, but many other milestone dates or times exist that have caused or will cause problems depending on various programming deficiencies.

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- "Time formatting and storage bugs" | 2021-12-26 | 47 Upvotes 2 Comments

# Symmetry Minute

The **symmetry minute** is a significant time point in the clock face timetables used by many public transport operators. At this point in the cycle, a train in a clock-face timetable meets its counterpart travelling in the opposite direction on the same line. If this crossing time is constant across a network, connecting times between lines are kept consistent in both directions.

At the symmetry time, the timetable is mirrored in both directions. At the ends of the line, the center of the turnaround time coincides with the symmetry minute. The distance between two consecutive symmetry times is equal to half the cycle time, so on an hourly schedule, opposite trains on the same line cross every 30 minutes. On a two-hour cycle, there is a symmetry time every hour.

In principle, a train-encounter can be set at any time. However, at the transition between two networks or lines, it is expedient to set uniform symmetry minutes, to create a symmetrical connection relation. For the long-distance cycle systems of ÖBB and SBB, the Forschungsgesellschaft für Straßen- und Verkehrswesen für Deutschland (Research Association for Roads and Traffic for Germany) recommends minute 58, so a four-minute minimum connecting time results in a departure at minute 0. Meanwhile, most railways in Central Europe and a number of other transport operators have established the symmetry minute 58½, for a three-minute hold time before a departure at minute 0. Shorter cycles have additional symmetry minutes, shifted by half the cycle time. So an hourly cycle has symmetries at minutes 28½ and 58½, a 30-minute cycle has symmetries at minutes 13½, 28½, 43½ and 58½, and so on.

The following table shows the departure times in opposite directions for an hourly cycle, using the 58½ symmetry minute (the most common in Central Europe). The other departure times for shorter cycles can be calculated from it. The last line gives the meeting times.

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- "Symmetry Minute" | 2019-07-18 | 84 Upvotes 18 Comments

# Rømer's determination of the speed of light (1676)

**Rømer's determination of the speed of light** was the demonstration in 1676 that light has a finite speed and so does not travel instantaneously. The discovery is usually attributed to Danish astronomer Ole Rømer, who was working at the Royal Observatory in Paris at the time.

By timing the eclipses of the Jovian moon Io, Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun. This would give light a velocity of about 220,000 kilometres per second, about 26% lower than the true value of 299,792 km/s.

Rømer's theory was controversial at the time that he announced it and he never convinced the director of the Paris Observatory, Giovanni Domenico Cassini, to fully accept it. However, it quickly gained support among other natural philosophers of the period such as Christiaan Huygens and Isaac Newton. It was finally confirmed nearly two decades after Rømer's death, with the explanation in 1729 of stellar aberration by the English astronomer James Bradley.

# Schönhage–Strassen Algorithm

The **Schönhage–Strassen algorithm** is an asymptotically fast multiplication algorithm for large integers. It was developed by Arnold Schönhage and Volker Strassen in 1971. The run-time bit complexity is, in Big O notation, $O(n\cdot \log n\cdot \log \log n)$ for two *n*-digit numbers. The algorithm uses recursive fast Fourier transforms in rings with 2^{n}+1 elements, a specific type of number theoretic transform.

The Schönhage–Strassen algorithm was the asymptotically fastest multiplication method known from 1971 until 2007, when a new method, Fürer's algorithm, was announced with lower asymptotic complexity; however, Fürer's algorithm currently only achieves an advantage for astronomically large values and is used only in Basic Polynomial Algebra Subprograms (BPAS) (see Galactic algorithms).

In practice the Schönhage–Strassen algorithm starts to outperform older methods such as Karatsuba and Toom–Cook multiplication for numbers beyond 2^{215} to 2^{217} (10,000 to 40,000 decimal digits). The GNU Multi-Precision Library uses it for values of at least 1728 to 7808 64-bit words (33,000 to 150,000 decimal digits), depending on architecture. There is a Java implementation of Schönhage–Strassen which uses it above 74,000 decimal digits.

Applications of the Schönhage–Strassen algorithm include mathematical empiricism, such as the Great Internet Mersenne Prime Search and computing approximations of *π*, as well as practical applications such as Kronecker substitution, in which multiplication of polynomials with integer coefficients can be efficiently reduced to large integer multiplication; this is used in practice by GMP-ECM for Lenstra elliptic curve factorization.

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- "Schönhage–Strassen Algorithm" | 2022-07-14 | 58 Upvotes 7 Comments

# Cephalization

**Cephalization** is an evolutionary trend in which, over many generations, the mouth, sense organs, and nerve ganglia become concentrated at the front end of an animal, producing a head region. This is associated with movement and bilateral symmetry, such that the animal has a definite head end. This led to the formation of a highly sophisticated brain in three groups of animals, namely the arthropods, cephalopod molluscs, and vertebrates.

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- "Cephalization" | 2020-07-23 | 14 Upvotes 2 Comments