Quad
The Quadrilateral Security Dialogue, commonly known as the Quad, is an informal diplomatic partnership comprising Australia, India, Japan, and the United States, focused on advancing a free, open, inclusive, and resilient Indo-Pacific region through cooperation on shared challenges such as maritime security, critical technologies, climate resilience, and public health.[1][2][3] The partnership traces its origins to collaborative humanitarian efforts following the 2004 Indian Ocean tsunami, which laid the groundwork for initial senior-level dialogues among the four nations in 2007, though the grouping lapsed amid domestic political shifts, particularly in Australia.[2][4] It was revived in 2017 at the vice-ministerial level and elevated to leaders' summits by 2021, reflecting heightened regional tensions and a mutual commitment to counterbalance assertive maritime claims without forming a formal military alliance or mutual defense pact.[5][6] Key initiatives include joint working groups on areas like vaccine delivery during the COVID-19 pandemic, infrastructure standards to promote transparent development, and maritime domain awareness exercises to enhance situational transparency in shared waters.[7][8] The Quad's activities emphasize practical outcomes over institutionalization, with annual foreign ministers' meetings—most recently in 2025—addressing supply chain resilience and disaster response capabilities, though it faces criticism from observers in China and elsewhere as an effort to contain Beijing's influence, a characterization the partners reject in favor of a positive regional agenda.[1][9][3]International Relations and Security
Quadrilateral Security Dialogue
The Quadrilateral Security Dialogue, commonly known as the Quad, is an informal strategic partnership comprising Australia, India, Japan, and the United States. Established to promote a free, open, and inclusive Indo-Pacific region, it addresses shared concerns including maritime security, supply chain resilience, critical technologies, and humanitarian assistance. Unlike formal alliances such as NATO, the Quad operates without a treaty or mutual defense commitments, emphasizing cooperation on practical initiatives rather than military confrontation.[2][5] The initiative originated in 2007 when Japanese Prime Minister Shinzo Abe proposed a quadrilateral dialogue, building on prior tsunami relief cooperation among the four nations following the 2004 Indian Ocean earthquake. Initial meetings occurred in 2007, involving foreign ministers from Australia, India, Japan, and the United States, but the grouping lapsed after Australia's change in government in 2007 and amid diplomatic sensitivities. It was revived in 2017 as "Quad 2.0," driven by escalating regional tensions, including China's territorial assertions in the South China Sea and assertive maritime behavior. Senior officials resumed dialogues that year, with foreign ministers meeting in September 2019 in New York.[4][9] The first Quad Leaders' Summit took place virtually on March 12, 2021, hosted by U.S. President Joe Biden, marking elevation to head-of-government level. Subsequent in-person summits occurred in Washington, D.C. (September 2021), Tokyo (May 2022), Hiroshima (May 2023), and Wilmington, Delaware (September 2024), focusing on deliverables such as the Quad Vaccine Partnership for COVID-19 distribution in the region (delivering over 500 million doses by 2022), maritime domain awareness initiatives using satellite data to monitor illegal fishing, and infrastructure projects under the Quad Infrastructure Coordination Group. In 2023, leaders committed to expanding STEM scholarships for 50,000 students from the region by 2030 and advancing clean energy transitions, including green shipping corridors. The 2024 summit emphasized cybersecurity, undersea cable connectivity, and joint disaster response capabilities. The next Leaders' Summit is scheduled for India in 2025, with the U.S. hosting foreign ministers that year.[2][10][1] Quad objectives center on upholding international law, particularly freedom of navigation under the United Nations Convention on the Law of the Sea, and countering coercive economic practices through diversified supply chains for semiconductors and rare earths. Working groups address health security, climate change, and critical technologies like 5G and AI standards. While not explicitly anti-China, the framework responds to empirical patterns of unilateral actions, such as island-building and militarization in disputed seas, which have heightened regional instability. China's official responses have evolved from dismissing the Quad as "sea foam" in 2018 to portraying it as an "Asian NATO" aimed at containment, reflecting Beijing's strategic concerns over encirclement. Independent analyses note that the Quad's ambiguity on military roles mitigates escalation risks while enabling substantive outputs, though its effectiveness depends on sustained political will amid domestic priorities in member states.[2][11][12]Human Anatomy and Medicine
Quadriceps Femoris
The quadriceps femoris is a large muscle group situated on the anterior and lateral aspects of the thigh, comprising four distinct heads that collectively form the primary extensor of the knee joint.[13] [14] These muscles originate proximally from the pelvis and femur, converge into a common tendon that inserts onto the patella and tibial tuberosity via the patellar ligament, enabling forceful leg extension essential for locomotion, standing, and athletic activities.[15] [16] The group is innervated by the femoral nerve (L2-L4 spinal segments), which provides motor supply to all four heads, ensuring coordinated contraction for knee stabilization and extension.[17] [15] The four muscles include:- Rectus femoris, which spans both the hip and knee joints, originating from the anterior inferior iliac spine and acetabular rim, contributing to hip flexion in addition to knee extension.[13] [14]
- Vastus lateralis, the largest head, arising from the lateral linea aspera and gluteal tuberosity of the femur, positioned laterally to provide lateral knee stability.[17] [18]
- Vastus medialis, originating from the medial linea aspera and intertrochanteric line, inserting medially to counteract lateral patellar deviation and support medial knee stability.[13] [16]
- Vastus intermedius, lying deep to the rectus femoris along the anterior femoral shaft, aiding in overall knee extension without crossing the hip joint.[14] [18]
Land Vehicles and Transportation
Quad Bike
A quad bike, also known as a quadricycle or four-wheeler, is a small motorized off-road vehicle featuring four low-pressure tires, a straddle seat, and handlebar steering, designed primarily for traversing rough terrain.[25] Unlike utility task vehicles (UTVs), quad bikes lack enclosed cabs or side-by-side seating, emphasizing maneuverability over passenger capacity or load-hauling in their standard form. They typically weigh under 550 kg and are powered by single-cylinder engines ranging from 50 cc to over 1,000 cc, with configurations including two-wheel or four-wheel drive.[26] The origins of the quad bike trace to early 20th-century prototypes, but modern development accelerated in the 1960s with the Canadian Jiger, a six-wheeled amphibious vehicle weighing 200 pounds and powered by a 5.5-horsepower engine.[27] Three-wheeled precursors dominated initial commercialization, exemplified by Honda's ATC90 in 1970, which popularized the straddle-style ATV in the United States. The shift to four wheels for improved stability occurred in 1982 with Suzuki's introduction of the QuadRunner LT125, a rear-wheel-drive model with a 125 cc four-stroke engine and five-speed transmission, marking the first mass-produced four-wheeled ATV.[28] Subsequent innovations by manufacturers like Honda, Yamaha, and Polaris expanded options, incorporating independent suspension and fuel injection by the 1990s to enhance handling on diverse surfaces.[29] Quad bikes serve recreational purposes such as trail riding and racing, as well as utility roles in agriculture, hunting, and ranching, where models often include cargo racks capable of supporting 200-500 pounds.[30] Design features prioritize low center of gravity and wide wheelbases for traction, with tire pressures around 5-7 psi to distribute weight over soft ground; however, most lack inherent rollover protection, relying on operator skill to mitigate risks.[31] Safety concerns dominate quad bike usage, with rollovers accounting for a majority of fatalities due to the absence of standard roll bars or crush protection in base models.[32] In jurisdictions like the UK, regulations under the Provision and Use of Work Equipment Regulations 1998 mandate helmets and prohibit operation on public roads without modifications, while some regions require operator protection devices for agricultural use.[33] Empirical data from safety agencies highlight that proper training and adherence to terrain limits reduce injury rates, underscoring the vehicles' unsuitability for paved surfaces where control diminishes.[34]Quadricycle
A quadricycle is a four-wheeled motor vehicle classified under the European Union's L-category for lightweight powered vehicles, distinct from standard automobiles due to lower mass, power, and speed limits designed for urban and restricted-access use.[35] These vehicles encompass both internal combustion and electric propulsion systems and are subdivided into light quadricycles (L6e) and heavy quadricycles (L7e), with regulations harmonized across EU member states via Regulation (EU) No 168/2013, effective from January 2016.[35] The category originated in 1992 to formalize microcars and small utility vehicles previously lacking unified standards, enabling type approval for road use without full car homologation.[36] Light quadricycles (L6e) are limited to an unladen mass of no more than 350 kg (550 kg for goods transport), a maximum design speed of 45 km/h, and engine power not exceeding 4 kW for internal combustion or equivalent for electric variants.[37] Heavy quadricycles (L7e) allow greater capabilities, with unladen mass up to 400 kg (550 kg for passenger transport or 600 kg for goods), speeds up to 90 km/h, and power limits of 15 kW for internal combustion engines or a net power equivalent of 15 kW (factored by 1.25 for electric) after accounting for energy storage mass.[37] These distinctions reflect causal trade-offs in design: lighter models prioritize accessibility for novice drivers, often requiring only an AM license (for ages 15-18 in many EU countries), while heavier ones demand a B1 or full B license and offer marginally better performance for short-haul tasks.[38] Emissions standards align with Euro 5 for light and Euro 4 for heavy models, though electric variants face fewer constraints.[39] Historically, the term "quadricycle" traces to late-19th-century prototypes like Henry Ford's 1896 gasoline-powered Quadricycle, a rudimentary four-wheeled frame with a 2.28 kW engine achieving 20 mph, marking an early step in automotive evolution from bicycles.[40] Modern quadricycles, however, emerged as a regulatory niche in post-war Europe amid fuel shortages, evolving from 1950s-1970s microcars (e.g., Messerschmitt or Isetta derivatives) into standardized vehicles by the 1990s to address urban congestion and licensing barriers.[41] Market adoption surged in countries like France and Italy, where brands such as Aixam, Ligier, and Microcar dominate, with annual EU sales exceeding 20,000 units as of 2023, primarily for personal mobility and delivery.[42] Safety standards for quadricycles lag behind those for passenger cars, with no mandatory frontal or side crash testing required for L6e models and only basic UNECE provisions for L7e, leading to structural vulnerabilities in collisions.[43] Euro NCAP assessments from 2014-2016 rated tested quadricycles at zero to two stars, citing poor adult occupant protection in 50 km/h impacts due to inadequate crumple zones and lightweight frames incompatible with heavier traffic.[44] [45] Usage data indicates higher injury risks for quadricycle occupants versus car users, attributed to mass mismatches in mixed fleets, though proponents argue their low speeds mitigate real-world severity in urban settings.[46] Recent EU updates from 2021 impose stricter market surveillance but retain exemptions from full vehicle safety directives.[47]Computing and Technology
Quad-Core Processor
A quad-core processor is a central processing unit (CPU) consisting of four independent processing cores integrated onto a single chip, enabling simultaneous execution of multiple threads or instructions to improve overall system performance.[48] Each core operates as a separate processor with its own arithmetic logic unit (ALU), control unit, and registers, while typically sharing higher-level caches and the system bus for data access.[49] This architecture leverages parallelism to handle workloads more efficiently than single- or dual-core designs, particularly in multi-threaded environments, though benefits depend on software optimization for core utilization.[50] The development of quad-core processors emerged as an extension of multi-core technology to address the limitations of increasing clock speeds under power and thermal constraints, following Dennard scaling breakdowns in the mid-2000s. Intel released its first desktop quad-core processors, the Core 2 Quad series (code-named Kentsfield), on November 2, 2006, featuring 65 nm process technology and dual-die configurations with 8 MB of L2 cache.[51] AMD followed with its Phenom X4 quad-core lineup in late 2007, using a monolithic die design on 65 nm, which offered better inter-core communication latency compared to Intel's initial multi-chip module approach.[52] In mobile and embedded systems, ARM-based quad-core processors gained traction earlier, with designs like NVIDIA's Tegra 3 (Kal-El) in 2011 introducing variable symmetric multiprocessing for power efficiency.[53] Quad-core processors provide advantages in multitasking and parallel computing tasks, such as video encoding, 3D rendering, and scientific simulations, where workloads can be distributed across cores to reduce execution time by up to fourfold in ideal scenarios.[50] They also enable better power management in battery-constrained devices by allowing inactive cores to enter low-power states, as seen in ARM architectures used in smartphones.[52] However, drawbacks include diminished returns for single-threaded applications, where performance relies more on per-core clock speed than core count, and increased complexity in cache coherence protocols like MESI, which can introduce overhead in inter-core data sharing.[50] Early quad-core implementations, such as Intel's 2006 models, consumed higher power (up to 130W TDP) without proportional gains in single-thread efficiency, highlighting the need for software adaptations.[51] Prominent examples include Intel's Core i5-750 (released September 8, 2009, with 2.66 GHz base clock and 95W TDP) for desktops, AMD's Ryzen 3 series quad-core variants for budget computing, and ARM-based chips like Qualcomm Snapdragon 400 series (introduced 2013) for mobile devices, which prioritize efficiency over raw power.[54] By 2025, quad-core configurations persist in entry-level and embedded systems, such as IoT devices and low-end laptops, though higher core counts dominate high-performance segments due to continued scaling in process nodes like 5 nm and below.[52]Architecture and Urban Design
Quadrangle
A quadrangle is a rectangular or square open courtyard enclosed by buildings on four sides, typically serving as a communal space within academic, monastic, or civic complexes. This layout fosters interaction, contemplation, and protection from external elements, with origins tracing to enclosed monastic cloisters in medieval Europe that adapted Roman atrium designs for collective living and study.[55][56] The concept gained prominence in university architecture during the late 14th century, with the first deliberately planned quadrangle completed in 1403 at New College, Oxford, founded in 1379 by William of Wykeham. This three-sided front quad marked a shift toward organized educational enclosures, influencing subsequent designs at institutions like St. John's College, Oxford, where the Canterbury Quadrangle (built 1631–1636) introduced Italian Renaissance elements such as arcades and symmetry. In the United States, quadrangles proliferated in the late 19th and early 20th centuries under Collegiate Gothic style, exemplified by the University of Pennsylvania's Quadrangle dormitories (constructed 1894–1929 in Tudor Gothic by Cope and Stewardson) and the University of Chicago's Main Quadrangle (designed by Henry Ives Cobb, with core structures by 1910).[57][58][59] Architecturally, quadrangles emphasize axial symmetry, uniform building heights, and peripheral walkways, often incorporating gateways, lawns, and fountains to enhance spatial enclosure and visual harmony. These features promote pedestrian flow and outdoor gatherings while maintaining privacy, as seen in the University of Rhode Island's Quadrangle, where granite buildings from 1892 onward form a cohesive historic core. Modern adaptations, such as glazed enclosures or integrated green spaces, preserve the archetype but adapt to contemporary needs like expanded social areas.[60][61]Sports and Physical Activities
Quad Jump
A quadruple jump, or quad, in figure skating is an airborne element in which the skater completes four full revolutions before landing on a single foot, executed from either the left or right foot depending on the skater's rotation direction.[62] These jumps demand precise timing, rotational speed exceeding 300 degrees per second, and significant lower-body power, with takeoff velocities around 5-6 meters per second and air times of approximately 0.6-0.7 seconds.[63] The biomechanics involve rapid pre-rotation on the ice, tight aerial positioning to minimize moment of inertia, and controlled landing to absorb forces up to 8-10 times body weight, primarily through knee and hip flexion.[64] The first ratified quad jump in competition history was a toe loop landed by Canadian skater Kurt Browning at the 1988 World Figure Skating Championships in Budapest, Hungary, on March 25, 1988.[65] Prior attempts, such as those by American skaters in the early 1980s, were under-rotated and not officially recognized under International Skating Union (ISU) rules requiring full rotation.[66] Quad jumps proliferated in the 1990s and 2000s, with toe loops and Salchows being the most common due to their takeoff mechanics allowing greater rotational momentum from the free leg.[67] Six jump types exist in figure skating: toe loop, flip, Lutz, Salchow, loop, and Axel. All but the Axel have been executed as clean quads in competition, with the quad Axel—requiring four-and-a-half revolutions due to its forward takeoff—first landed cleanly by American skater Ilia Malinin at the 2022 U.S. Classic on September 15, 2022.[68] Lutz and flip jumps, edge jumps involving outside edges, pose higher technical demands and lower success rates owing to the need for precise blade placement to avoid "flutzing" or "flipping," where the skater takes off from the incorrect edge.[69] In women's figure skating, Japanese skater Miki Ando became the first to land a quad Salchow in international competition at the 2002 Junior Grand Prix Final in The Hague, Netherlands, on December 13, 2002.[70] Russian skater Kamila Valieva was the first woman to land a quad at the Olympics, executing a Salchow during the team event free skate at the 2022 Beijing Winter Olympics on February 7, 2022.[71] Adoption of quads by female skaters accelerated post-2018, driven by Russian training methodologies emphasizing early technical progression, though this has correlated with elevated injury risks from repetitive high-impact loading on growing skeletons, including stress fractures and sacroiliac joint dysfunction.[72] Contemporary records highlight escalating complexity: Malinin achieved the first program with all six quad types (toe loop, Salchow, loop, flip, Lutz, and Axel) during the 2025 ISU World Figure Skating Championships free skate in Boston, Massachusetts, on March 29, 2025, while also tying the record for six quads in a single program, a feat he repeated at the 2025 U.S. Figure Skating Championships on January 26, 2025.[73][74] These performances underscore causal factors in quad execution, such as optimized body composition, plyometric strength training, and harness-assisted practice to build aerial control without full landing impact.[63] However, under ISU scoring, quads yield base values from 9.5 (toe loop) to 12.3 (Axel) points, incentivizing their inclusion despite fall risks that deduct up to 1.0 points per error and potential long-term joint wear from asymmetric loading.[75]Quad Rugby
Quad rugby, also known as wheelchair rugby outside the United States, is a full-contact, mixed-gender team sport designed for athletes with tetraplegia or impairments affecting function in all four limbs. It integrates elements of rugby's physicality, basketball's ball-handling, and hockey's speed, played indoors using specialized manual wheelchairs that enable aggressive wheelchair-to-wheelchair collisions. The objective is to score by advancing a volleyball-sized ball across the opponent's goal line while in possession, either by carrying or passing.[76][77] The sport was invented in 1977 in Winnipeg, Canada, by quadriplegic athletes seeking a more dynamic alternative to wheelchair basketball, initially naming it "murderball" to reflect its combative style. It reached the United States in 1981, where it adopted the term quad rugby, leading to the formation of the United States Quad Rugby Association (later renamed United States Wheelchair Rugby Association) in 1988 to standardize rules and foster growth. Internationally, the World Wheelchair Rugby (WWR), established in 1993 as the International Wheelchair Rugby Federation, serves as the global governing body, overseeing competitions in over 40 countries across Americas, Europe, and Asia-Oceania zones. Quad rugby appeared as a demonstration event at the 1996 Atlanta Paralympic Games and achieved full medal status at the 2000 Sydney Paralympics.[78][79][80] Matches occur on a basketball court sized 28 meters long by 15 meters wide, divided by a centerline with key areas at each end measuring 8 meters wide by 1.75 meters deep. Each team fields four players on the court from a roster of up to 12, with games structured as four 8-minute quarters separated by brief halftimes. Possession is limited to 40 seconds, after which the ball turns over; players cannot dribble but must pass or carry the ball, advancing only while holding it. Physical contact is integral, permitting wheelchair rams to dislodge opponents or the ball, though illegal hits like spearing or reaching incurs penalties.[77][81][82] Player eligibility requires significant impairments in three or more limbs, assessed via a classification system assigning points from 0.5 (severest limitations in trunk control, arm propulsion, and grasping) to 3.5 (milder impairments allowing greater mobility and handling). The four on-court players' total classification points must not exceed 8.0, promoting balanced teams reliant on tactical combinations rather than individual ability alone. Classifications are determined through medical evaluation and functional testing, updated periodically to reflect changes in impairment.[83][84][85] Equipment includes custom wheelchairs with low-profile seats for stability, cambered rear wheels for agility, forward-positioned drive rings, and protective bumpers; anti-tip casters at the rear prevent flips during impacts. The ball is a size-5 volleyball, and protective gear like mouthguards and gloves is mandatory, with helmets optional. These adaptations enable high-speed play reaching 30 km/h and forces equivalent to car crashes in collisions, underscoring the sport's demand for durable, athlete-specific designs.[77][86]Arts, Entertainment, and Media
Quad (The Who Album)
Quad, also known as Quads, was an unfinished rock opera concept developed by Pete Townshend for the English rock band The Who in 1966.[87] Set in an alternate future year of 1999, the narrative explored a dystopian society enabled by genetic engineering, where parents could predetermine the sex of their offspring.[88] The central plot followed a family that requested four daughters but received three girls and one boy due to an error, leading the boy—raised as a girl—to grapple with identity conflict, rebellion, and psychological turmoil.[89] This early project marked Townshend's initial foray into extended conceptual storytelling, predating the band's more realized rock opera Tommy by three years and influencing the development of the rock opera format.[90] Townshend conceived Quad amid The Who's rapid evolution from singles-oriented pop to ambitious compositions, drawing from his interest in thematic narratives and social commentary.[87] Recording efforts were limited, with no full band sessions documented for the project; instead, Townshend focused on demos and individual tracks. The concept stalled due to creative challenges, including the difficulty of sustaining a cohesive multi-song storyline, and the band's immediate commercial pressures under manager Kit Lambert, who pushed for hit singles.[91] By mid-1966, Townshend shifted priorities, salvaging elements for standalone releases rather than pursuing the opera's completion.[92] The sole surviving song directly tied to Quad is "I'm a Boy," a demo of which Townshend recorded in 1966, depicting the protagonist's anguish over his imposed femininity: "I'm a boy, I'm a boy, but my ma won't admit it."[87] Released as a single on 9 September 1966 via Reaction Records, it peaked at No. 2 on the UK Singles Chart despite its provocative lyrics, which Lambert initially resisted for potential backlash.[91] Other songs potentially linked, such as elements from the A Quick One mini-opera, were repurposed but not core to Quad's storyline. No comprehensive tracklist or full demos have surfaced publicly, underscoring the project's embryonic status.[90] Abandonment of Quad reflected broader tensions in The Who's creative process during 1966–1967, as Townshend balanced innovation with market demands; the band prioritized A Quick One (1966) to fill contractual obligations.[92] Townshend later reflected on it as an exploratory failure that honed his songwriting for future works like Tommy, though he has not revisited it in subsequent interviews or releases.[93] Its legacy endures in discussions of The Who's pioneering role in rock operas, highlighting themes of gender and identity that anticipated later cultural debates, albeit rooted in speculative fiction rather than contemporary activism.[87] No official album materialized, leaving Quad as a footnote in the band's discography of unrealized ambitions.[94]Quad (Other Media Works)
Quad is a silent television play written by Samuel Beckett, consisting of two parts: Quad I, performed at a fast tempo, and Quad II, at a slow tempo featuring only the first series of movements.[95] The work involves four performers clad in hooded robes of distinct colors—white, yellow, blue, and black—who traverse the diagonals, sides, and center of an empty square platform in a precisely choreographed pattern of 16 permutations, without intersecting or speaking.[96] Accompanied by percussion, the piece explores themes of repetition, absence, and geometric abstraction, reflecting Beckett's late minimalist style.[97] First transmitted on December 16, 1982, by Süddeutscher Rundfunk (now part of Südwestrundfunk) under the title Quadrat 1 + 2, the original production ran approximately 15 minutes for Quad I and featured no dialogue, emphasizing visual and rhythmic elements over narrative.[96] Beckett directed the work himself, drawing from influences like mathematical permutations and his interest in non-verbal expression, as seen in earlier pieces such as Act Without Words.[98] The play has been restaged infrequently due to its brevity and abstract demands, including a 2020 production at UCLA directed by Michael Hackett, which highlighted its distillation of human movement into elemental patterns.[99] A separate short film titled Quad (2016), directed by Chop Mosley, depicts a couple engaging in thrill-seeking activities but lacks connection to Beckett's work and received limited distribution.[100] No other major media works titled Quad—such as novels, series, or video games—have achieved comparable prominence, with most references in gaming or film contexts pertaining to vehicular or action genres rather than titled properties.[101]Business and Industry
Quad (Printing Company)
Quad is a global marketing experience company specializing in print production, media solutions, and integrated marketing services, headquartered in Sussex, Wisconsin. Founded on July 13, 1971, by Harry V. Quadracci as Quad/Graphics, it began operations in a vacant manufacturing facility in Pewaukee, Wisconsin, with initial funding from a second mortgage on Quadracci's home and a single printing press.[102][103] The company initially focused on commercial printing, emphasizing technological innovation to solve production challenges for brands.[102] Over decades, Quad expanded through acquisitions and diversification beyond traditional printing into multichannel marketing, including digital production, creative agency services, strategic consulting, and logistics. By 1987, it had secured major contracts, such as printing People magazine, establishing itself as a leading printer of newsweeklies.[104] The firm rebranded to Quad in 2023, reflecting its evolution into a full-service marketing provider serving sectors like retail, automotive, and publishing with clients including Adidas, Chevrolet, and Toyota.[105][102] It operates manufacturing and distribution facilities across North America, Europe, Asia, and other regions, functioning as a 24/7 platform for end-to-end solutions from concept to delivery.[106] As a publicly traded entity on the New York Stock Exchange under the ticker QUAD, the company reported net sales of $2.7 billion for fiscal year 2024, down from $3.0 billion in 2023, amid a net loss of $51 million.[107] Quad employs approximately 12,200 people as of December 31, 2024, across more than 11 countries, serving over 2,100 clients.[108][109] It ranks as the second-largest commercial printer in North America and the 14th-largest agency company in the U.S. according to Ad Age's 2023 rankings.[110] Current leadership includes Chairman, President, and CEO Joel Quadracci, son of the founder, who oversees a culture emphasizing employee empowerment and client-focused innovation.[106]Typography and Printing
Quadrat
A quadrat, also known as a quad, is a rectangular piece of type metal employed in letterpress typesetting to create blank spaces.[111] Its body height matches that of the typeface being used, typically 0.918 inches in Anglo-American systems, but the face is recessed below printing height to avoid inking and impression.[112] Composed of a type metal alloy including lead, tin, and antimony, quadrats provide structural support under printing pressure while remaining non-printing.[113] The em quadrat, or em quad, measures squarely equal to the point size of the type body—for instance, a 12-point em quad is 12 points wide by 12 points high—and serves as the foundational spacing unit.[113] [112] The en quadrat, or en quad, is half that width, approximately matching the width of an uppercase N in historical typefaces.[113] Larger variants include two-em, three-em, and four-em quadrats, with the latter being the largest commonly cast, used for extending short lines or creating wider separations; sizes were limited by type family, such as four-em quadrats available only up to pica size.[111] Finer spaces, like three-to-the-em (one-third em width), supplemented these for word separation.[112] Historically documented by Joseph Moxon in his 1683–1684 Mechanick Exercises on the Whole Art of Printing, quadrats originated as essential tools for manual composition, enabling compositors to indent paragraphs, space words evenly, fill incomplete lines, form white rules, and justify tabular matter.[113] [111] In practice, em quads often framed lines in composing sticks to maintain tension, with thinner spaces distributed internally for adjustability.[112] Though supplanted by digital methods, the nomenclature persists in modern typography for relative spacing units, such as the em space equivalent to current font metrics.[113]Other Specialized Uses
Quad in Mathematics and Geometry
A quadrilateral, commonly abbreviated as "quad" in geometric contexts, is a two-dimensional polygon with exactly four sides, four vertices, and four angles. The term originates from the Latin words "quadri" (meaning four) and "lateralis" (meaning sided), emphasizing its four-edged structure. Unlike triangles, quadrilaterals are not necessarily regular, and their sides and angles can vary, but the sum of interior angles always totals 360 degrees, derived from the general polygon angle sum formula (n-2) \times 180^\circ where n=4.[114][115][116] Quadrilaterals are classified into convex and concave types based on their interior angles and vertex positions. Convex quadrilaterals have all interior angles less than 180 degrees, with no sides bending inwards, allowing a line segment between any two points inside to lie entirely within the shape. Concave quadrilaterals, by contrast, feature one interior angle exceeding 180 degrees (a reflex angle), causing one vertex to lie inside the figure formed by the other three. This distinction affects properties like diagonal intersection: in convex quads, diagonals cross inside the shape, whereas in concave ones, one diagonal may lie outside.[117][118] Specialized quadrilaterals exhibit additional symmetries and properties, forming a hierarchy of subtypes:- Trapezoid (or trapezium in some regions): Exactly one pair of parallel sides.[114]
- Parallelogram: Two pairs of parallel sides, with opposite angles equal and consecutive angles supplementary.[116]
- Rectangle: A parallelogram with four right angles (90 degrees each).[114]
- Rhombus: A parallelogram with all sides equal in length.[114]
- Square: A rectangle (or rhombus) with equal sides and right angles, possessing the highest symmetry among quadrilaterals.[116]
- Kite: Two pairs of adjacent equal sides, often with perpendicular diagonals where one bisects the other.[118]