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Net

A net is most commonly a device or textile consisting of an open-meshed material made by tying knots in string or cord, or by weaving threads together at right angles. Net may also refer to:
  • [[Physical nets|Physical nets]]: Including devices for catching or containing and netting fabrics.
  • [[Mathematical concepts]]: Such as a polyhedron net or topological net.
  • [[Economic terms]]: Including net in economics and net income.
  • [[Computing terms]]: Such as a computer network or the Internet.
  • [[Other meanings]]: Including sports and safety applications, and arts and media.

Physical nets

Device

A net is a flexible, open-meshed constructed from knotted , cord, , or wire, forming a series of interconnected loops or meshes designed to capture, contain, or secure objects while allowing smaller items or fluids to pass through. The origins of nets trace back to prehistoric times, primarily for and , with the earliest unambiguous evidence from engravings in depicting fish caught in nets around 15,800 years ago. The oldest preserved physical net, known as the Antrea Net, dates to approximately 8,500 BCE and was discovered in , consisting of willow bark cords used for . Nets are typically made by hand-knotting strands of material, employing techniques such as the (a variant often used in netting to join meshes securely) and occasionally the for initial attachments or securing ends. Common materials include natural fibers like and historical plant-based cords, as well as modern synthetics such as and , which provide durability, resistance to rot, and varying levels of elasticity depending on the application. In fishing, nets serve as primary tools for capturing aquatic species, with types like drift nets—free-floating gillnets that entangle by their gills—and gillnets deployed vertically in the to target schooling pelagics. Mesh sizes in these nets are regulated by international agreements and national authorities, guided by FAO recommendations, with minimum dimensions varying by and ; for example, at least 100 mm in some cod-end regulations for demersal trawls to allow to escape while retaining adults. Beyond fishing, nets are used for terrestrial animals, such as in where camouflaged ensnares birds or small mammals without harm. Industrially, heavy-duty nets secure during transport, preventing loads from shifting in ships, trucks, or . Representative examples include the butterfly net, a lightweight, conical mesh device with a long handle used by entomologists for gently capturing in flight during field collection. Another is the cargo net, a robust, knotted or mesh applied in shipping to restrain pallets, vehicles, or bulk goods on decks or in holds, ensuring stability against motion and weather.

Textile

Net fabric, also known as netting, is a lightweight characterized by an open-mesh structure formed through loosely woven or knitted yarns that create large, uniform openings between intersections, setting it apart from denser knotted meshes typically used in other applications. This construction allows for breathability, transparency, and flexibility, making it suitable for aesthetic and functional purposes rather than heavy-duty restraint. The manufacturing of net fabrics involves interlacing yarns via machine weaving on specialized looms, such as raschel or tricot knitting machines, or through hand-crocheting for custom, intricate pieces. In contemporary industrial production, synthetic fibers like and dominate due to their strength, resistance to wear, and affordability, enabling high-volume output for diverse uses. Historically, openwork net-like textiles emerged in around 3000 BCE, appearing in ornate burial garments as precursors to . Significant advancement occurred in the with Heathcoat's 1809 invention of the bobbinet machine, which mechanized the production of fine, uniform net fabrics and revolutionized . Net fabrics find wide application in , where variants like provide sheer layers for veils, gowns, and dresses, enhancing visual lightness and drape. In home decor, they form airy curtains that diffuse light and hammocks offering supportive, ventilated seating. For protection, mosquito nets made from fine mesh are impregnated with insecticides such as pyrethroids, significantly reducing transmission by repelling and killing mosquitoes during sleep. Notable variants include bobbinet, a machine-produced hexagonal originally from but now often , prized for its stability in and foundations. Fishnet , featuring bold diamond openings, gained prominence in mid-20th-century fashion during the , symbolizing bold, provocative style in mainstream and performative attire.

Mathematical concepts

Polyhedron net

A net is a two-dimensional formed by unfolding the surface of a three-dimensional along its edges and laying it flat on a , such that the faces do not overlap and can be folded back to reconstruct the original without gaps or overlaps. This arrangement consists of the 's faces connected edge-to-edge in a connected, simply connected , effectively representing a cut-out that preserves adjacency relationships. The historical development of nets traces back to the , with early illustrations appearing in Dürer's 1525 treatise Underweysung der Messung mit dem Zirckel und Richtscheyt, where he depicted nets for polyhedra such as the and a to aid in geometric construction and artistic representation. By the , texts began incorporating nets more systematically for demonstrating polyhedral properties and facilitating the creation of physical models, reflecting their growing role in mathematical . Constructing a valid polyhedron net requires connecting the faces edge-to-edge to form a tree-like structure in the dual graph of the polyhedron, ensuring the pattern remains simply connected and free of interior holes. For convex polyhedra, additional rules prevent overlaps during folding, such as avoiding cycles longer than 4 in the face arrangement, which could cause intersecting faces; linear chains of faces are also limited based on the polyhedron's geometry to maintain foldability without self-intersection. Representative examples illustrate the variety of nets. For a , there are exactly 11 distinct nets up to , including cross-shaped patterns with a central square surrounded by four adjacent squares and two more attached to opposite arms, or zigzag s of six squares that fold without overlap. A has two distinct nets, one featuring four equilateral triangles arranged in a , which folds by bringing the end triangles together to form the apex. The admits 43,380 distinct nets, highlighting the combinatorial complexity for polyhedra with more faces. Polyhedron nets find practical applications in , where they help students visualize and manipulate three-dimensional shapes by constructing models to understand surface area and folding mechanics. In packaging design, nets serve as templates for efficient material cutouts that minimize waste and ensure structural integrity when assembled into boxes or containers. Similarly, in , they provide blueprints for fabricating prototypes or components, such as in forming or architectural modeling.

Topological net

In mathematics, particularly in , a topological net is defined as a function from a —equipped with a reflexive, transitive, and directed partial order—to a , serving as a generalization of sequences to study limits and in abstract settings where sequences alone are inadequate, such as non-first-countable spaces. The , often denoted (D, \leq), ensures that for any two elements \alpha, \beta \in D, there exists \gamma \in D such that \gamma \geq \alpha and \gamma \geq \beta, allowing the net to "progress" toward limits in a generalized sense. The concept of nets originated with and H. L. Smith in their 1922 paper establishing a general theory of limits, initially termed Moore-Smith sequences, to extend beyond metric spaces. Key properties include , where a net (x_\alpha)_{\alpha \in D} in a X converges to a point x \in X if, for every neighborhood U of x, there exists \alpha_0 \in D such that x_\alpha \in U for all \alpha \geq \alpha_0; this "eventual" containment generalizes the tail behavior of sequences. Additionally, nets satisfy a for : a function f: X \to Y between topological spaces is continuous at x if and only if, for every net (x_\alpha) converging to x in X, the composed net (f(x_\alpha)) converges to f(x) in Y. Illustrative examples highlight nets' utility. A constant net, where x_\alpha = c for all \alpha \in D and some fixed c \in X, trivially converges to c, demonstrating immediate eventual containment in any neighborhood of c. A principal net indexed by the natural numbers under the usual order (\mathbb{N}, \leq) reduces precisely to a , recovering classical limits when D is cofinal with \mathbb{N}. In metric spaces like the real numbers \mathbb{R}, nets extend Cauchy completeness: a net is Cauchy if, for every \epsilon > 0, there exists \alpha_0 \in D such that d(x_\alpha, x_\beta) < \epsilon for all \alpha, \beta \geq \alpha_0, and in complete spaces, every Cauchy net converges. Nets find essential applications in for handling convergence in spaces lacking countable local bases, such as uncountable product topologies where sequences fail to detect limits—for instance, the net of finite-support functions in \mathbb{R}^\mathbb{R} (indexed by finite subsets of \mathbb{R}) converges pointwise but not uniformly. In functional analysis, they characterize weak topologies on Banach spaces, enabling the study of of sequences of functionals without relying on first-countability, as in Alaoglu's theorem where nets in the unit ball of the attain weak* limits.

Economic terms

Net in economics

In economics and accounting, the term "net" denotes the resultant balance after deducting costs, liabilities, or other subtractions from a gross figure, yielding an accurate measure of the effective or amount. This foundational concept isolates the value-adding or usable portion by removing extraneous elements, ensuring precise economic valuation across various applications. The relationship between net and gross is straightforward, governed by the arithmetic principle: \text{net} = \text{gross} - \text{deductions} Allowable deductions typically encompass items like taxes and depreciation, tailored to the specific economic context to reflect true economic contribution. The usage of "net" in economic contexts traces its origins to the early 15th century in English accounting practices, derived from the Old French "net," meaning clean or pure, to signify an amount cleared of deductions. This terminology evolved alongside the development of systematic bookkeeping, particularly with the formalization of double-entry methods in Luca Pacioli's 1494 treatise Summa de arithmetica, which emphasized reducing accounts to a "resto" or remainder for balanced financial records. Key examples illustrate the net concept's application. Net weight represents the mass of goods excluding packaging or tare, calculated as gross weight minus the container's weight, which is essential for and pricing. Similarly, net price is the final selling amount after subtracting discounts from the , providing a clear basis for transactions. In shipping, measures a vessel's capacity as less deductions for non-earning spaces like crew quarters and engine rooms. The principles underlying netting promote accurate economic assessment by focusing on productive components, as seen in international standards such as , which guides by requiring entities to net amounts when acting as agents rather than principals, thereby depicting the true economic substance of transactions. One specific application of this broad netting framework is , which applies the concept to profitability after expenses.

Net income

Net income, also known as net profit or the "bottom line," represents a company's or individual's total earnings after deducting all expenses, including (COGS), operating expenses, , taxes, and other deductions from . This metric serves as the primary indicator of financial profitability, reflecting the residual amount available for distribution to shareholders or reinvestment after fulfilling all operational and fiscal obligations. In corporate contexts, it is derived from the , providing a comprehensive view of performance over a specific period, such as a fiscal quarter or year. The standardization of net income reporting emerged in the United States during the 1930s through the development of Generally Accepted Accounting Principles (GAAP), prompted by the Securities Act of 1933 and the establishment of the Securities and Exchange Commission (SEC) to ensure transparent financial disclosures amid the Great Depression. Globally, the International Financial Reporting Standards (IFRS), which include detailed guidelines for net income presentation, gained widespread adoption starting in 2005, particularly with the European Union's mandate for listed companies to use IFRS for consolidated statements, harmonizing international accounting practices. These frameworks ensure consistency, comparability, and reliability in how net income is calculated and reported across jurisdictions. The calculation of net income typically follows a multi-step process outlined in the income statement: \text{Net Income} = \text{Revenue} - \text{COGS} - \text{Operating Expenses} - \text{Interest} - \text{Taxes} First, gross profit is computed as revenue minus COGS, which includes direct costs like materials and labor. Operating income (or EBIT) is then derived by subtracting operating expenses such as salaries, rent, and depreciation from gross profit. Finally, non-operating items like interest and taxes are deducted to arrive at net income. This structured breakdown allows stakeholders to isolate profitability at various operational levels. For corporations, net income margins in the averaged approximately 10.7% in 2024, illustrating the sector's typical profitability after deductions, with variations by industry—technology firms often exceeding 20% while utilities hovered around 5-7%. On a personal level, refers to take-home pay after payroll taxes and deductions, such as an annual salary of $60,000 yielding approximately $50,200 for a single filer in the U.S. after standard federal , , and in 2024. Net income is integral to financial analysis, forming the basis for key ratios like the net profit margin (\text{Net Profit Margin} = \frac{\text{Net Income}}{\text{Revenue}} \times 100), which measures efficiency in converting revenue to profit. It is essential for tax filings, where corporations report it on Form 1120 to determine taxable income, and for investor evaluations, such as earnings per share calculations. Unlike EBITDA, which excludes interest, taxes, depreciation, and amortization to focus on core operations, net income provides a fuller picture of actual cash available post-all liabilities, though it may be influenced by non-cash items like depreciation.

Computing terms

Computer network

A is a set of interconnected devices, such as , , and peripherals, linked via wired or media to enable the exchange of and resources. This interconnection allows devices to communicate, share , and access shared like printers or systems efficiently. At its core, a facilitates reliable transmission through standardized rules and arrangements, forming the backbone of modern communication. The historical development of computer networks traces back to the , launched in 1969 by the U.S. Department of Defense's Advanced Research Projects Agency (), which connected four university computers and demonstrated packet-switching for resilient data transfer. This evolved into broader in the 1970s, with the introduction of Ethernet in 1973 at Xerox PARC, a technology using coaxial cables for collision-detection-based communication. Ethernet was standardized in 1983 as , enabling commercial adoption and speeds starting at 10 Mbps, which laid the foundation for today's high-speed wired networks. Key components of a include nodes, which are the devices like computers or smartphones that generate and consume ; links, the physical or wireless connections such as Ethernet cables or signals that carry between nodes; protocols, standardized rules like the / suite that govern formatting, addressing, and reliable delivery; and topologies, the structural arrangements defining how nodes interconnect, such as (central hub-based for easy management), (fully interconnected for redundancy), or bus (linear shared medium for simplicity). These elements ensure efficient, scalable operation, with / emerging in the 1980s as the dominant suite for routing packets across diverse networks. Computer networks are classified by scale and purpose into types like Personal Area Networks (PANs), which connect devices within a 10-meter range, such as Bluetooth-enabled wearables; Local Area Networks (LANs), covering up to 100 meters in homes or offices via or Ethernet for local resource access; (MANs), spanning a or campus for interconnecting multiple LANs; and Wide Area Networks (WANs), extending globally like backbones using fiber for long-distance . These range from small-scale PANs to vast global systems, with the serving as the largest public . Applications of computer networks primarily revolve around data communication, enabling real-time exchange via , video calls, or browsing, and resource sharing, allowing multiple users to access centralized files, printers, or databases to reduce costs and improve . is integral, with measures like firewalls to and block unauthorized , protocols to protect , and intrusion detection systems to safeguard against threats in shared environments. As of , over 19 billion devices are connected globally, underscoring the scale of networked applications from homes to systems.

Internet

The is a worldwide system of interconnected computer networks that use the (TCP/IP) to communicate and share data across billions of devices globally. Often referred to colloquially as "the Net," it enables seamless exchange of information through standardized protocols, forming a decentralized without a central authority. This global network evolved from and origins, transitioning into a commercial powerhouse that underpins modern communication, commerce, and access. Key historical milestones include the adoption of TCP/IP on January 1, 1983, which standardized data transmission across ARPANET and other networks, marking the birth of the modern Internet. In 1989, British computer scientist Tim Berners-Lee invented the World Wide Web at CERN, introducing hypertext and browsers to make the Internet more accessible. Commercialization accelerated in the 1990s, with the U.S. National Science Foundation lifting restrictions on commercial traffic in 1991, the release of the Mosaic web browser in 1993, and the privatization of NSFNET in 1995, enabling widespread ISP services and e-commerce. By 2025, the Internet's user base exceeds 6 billion individuals, representing about 73% of the global population. The Internet's infrastructure relies on backbone providers, primarily networks that operate global high-capacity fiber-optic cables and exchange traffic without payment through agreements. Examples include , , and (formerly Level 3), which form the core of the Internet's "backbone" spanning undersea and terrestrial routes. Core protocols include , adopted by 35.9% of websites by November 2025 for faster, more reliable data transfer via , and the ongoing transition, with around 45% of global traffic using as of late 2025 to address address exhaustion. Access methods have advanced with fiber-optic offering multi-gigabit speeds in urban areas and wireless technologies like providing widespread mobile connectivity, while research focuses on terabit-per-second capabilities for future ultra-low latency applications. A defining feature of the is its decentralized structure, where no single entity controls , allowing resilient packet-switched and end-to-end . This enables diverse services such as for asynchronous communication via SMTP and streaming media platforms like , which deliver on-demand video to over 300 million paid memberships worldwide as of 2025. However, challenges persist, including the , with an estimated 2.6 billion people—primarily in low-income countries—lacking access in 2025, exacerbating inequalities in and economic . Cybersecurity threats have intensified, with the global average cost of breaches reaching $4.45 million in 2023, a 15% rise over three years, driven by and state-sponsored attacks that underscore vulnerabilities in this interconnected ecosystem. The nickname "the Net" originated in the late within early computer networking communities and gained popularity in , including the 1995 film The Net starring , which dramatized online hacking and surveillance. Economically, the contributes significantly to global growth, with the accounting for about 15% of world GDP, valued at approximately $16 trillion as of 2025.

Other meanings

Sports and safety applications

Nets play a crucial role in various sports, providing boundaries and goals that define play areas and scoring. In , the net divides the into two equal halves, standing 3 feet (0.914 meters) high at the center and 3 feet 6 inches (1.07 meters) high at the posts, spanning the full width of the —32 feet (9.75 meters) for singles and 36 feet (11 meters) for doubles—to ensure and prevent balls from crossing uncontrollably. In soccer, goal nets adhere to standards, measuring 24 feet (8 yards or 7.32 meters) wide and 8 feet (2.44 meters) high, a dimension standardized since the sport's early rules in 1863 to promote consistent gameplay across matches. Volleyball nets, regulated by the FIVB, are set at a height of 7 feet 11 5/8 inches (2.43 meters) for men and 7 feet 4 1/8 inches (2.24 meters) at the center, extending across the court's 29 feet 6 inches (9 meters) width to facilitate spiking and blocking maneuvers. The historical development of sports nets has significantly influenced gameplay safety and accuracy. Soccer goal nets were invented by Liverpool engineer John Alexander Brodie in 1889, patented in 1891, and first used in a competitive match on 10 January 1891 in a North vs. South international selection game in , replacing vague tape lines and allowing goalkeepers to more effectively track shots. In basketball, nets evolved from the original 1891 peach baskets introduced by , which required manual ball retrieval after each score, to open-bottom metal-ring nets by 1906, enabling continuous play and reducing game interruptions. These innovations addressed practical challenges in early sports, enhancing both spectator experience and player efficiency. Beyond athletics, nets serve critical safety functions in high-risk environments. In , safety nets provide fall protection under OSHA regulations, required for work areas more than 25 feet above lower levels, with mesh sizes not exceeding 6 inches by 6 inches to catch falling workers or without allowing passage. nets, often deployed in urban rescue operations, extend horizontally at least 8 feet from building perimeters and no more than below escape points, designed to support sudden impacts from evacuees. Stunt nets in the film industry, used for high-fall scenes, must withstand substantial loads, typically tested to support up to several thousand pounds per impact point to ensure performer during dynamic sequences. Modern safety and sports nets incorporate durable materials and rigorous testing protocols for reliability. High-tensile polyethylene (HDPE), valued for its UV resistance and strength-to-weight ratio, is widely used in both applications, offering elongation under load to absorb energy without tearing. Standards mandate impact resistance testing, such as drop tests where a 400-pound sandbag is released from heights up to 45 feet to simulate falls, verifying the net's ability to decelerate objects without failure and ensuring compliance with performance thresholds like 17,500 foot-pounds of energy absorption. Innovations in net technology have integrated sensors for enhanced functionality, particularly in . , introduced in professional in 2001, employs multiple high-speed cameras to track ball trajectories relative to the net and lines, providing umpires with accurate in/out decisions and reducing in close calls. Additional smart features, such as sensors in tennis nets, detect let cords by monitoring oscillations, alerting officials instantaneously and streamlining gameplay in tournaments.

Arts and media

In film and television, "net" has appeared in titles exploring themes of digital entrapment and cyber threats. The 1995 American thriller The Net, directed by and starring as a software analyst whose life is disrupted by a hacker conspiracy, popularized anxieties about online identity theft and virtual surveillance. In music, "net" features in band names and song titles symbolizing protection or connectivity. Ariana Grande's 2020 song "Safety Net," from her album Positions, uses the metaphor of a net as emotional support in a faltering , peaking at number 22 on the Hot 100. Literature and comics have employed "net" both literally and metaphorically to evoke entrapment or interconnection. In Herman Melville's 1851 novel Moby-Dick, nautical nets serve as symbols of the whalemen's perilous labor and the inescapable web of fate, particularly in chapters describing the try-works and line-handling. Other media references include historical broadcasting entities. The National Educational Television (NET) network, operating from 1952 to 1970 in the United States, was a nonprofit public broadcaster precursor to PBS, delivering educational programming to over 200 stations. Briefly, the internet's pervasive influence appears thematically in cyber-themed , such as stunt sequences involving physical nets in action to mimic digital falls.

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