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Compass (drawing tool)
Compass (drawing tool)
Compass (drawing tool)
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from Wikipedia
A beam compass and a regular compass
Using a compass
A compass with an extension accessory for larger circles
A bow compass capable of drawing the smallest possible circles

A compass, also commonly known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.

Prior to computerization, compasses and other tools for manual drafting were often packaged as a set[1] with interchangeable parts. By the mid-twentieth century, circle templates supplemented the use of compasses.[citation needed] Today those facilities are more often provided by computer-aided design programs, so the physical tools serve mainly a didactic purpose in teaching geometry, technical drawing, etc.

Construction and parts

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Compasses are usually made of metal or plastic, and consist of two "legs" connected by a hinge which can be adjusted to allow changing of the radius of the circle drawn. Typically one leg has a spike at its end for anchoring, and the other leg holds a drawing tool, such as a pencil, a short length of just pencil lead or sometimes a pen.

Handle

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The handle, a small knurled rod above the hinge, is usually about half an inch long. Users can grip it between their pointer finger and thumb.

Legs

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There are two types of leg in a pair of compasses: the straight or the steady leg and the adjustable one. Each has a separate purpose; the steady leg serves as the basis or support for the needle point, while the adjustable leg can be altered in order to draw different sizes of circles.

Hinge

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The screw through the hinge holds the two legs in position. The hinge can be adjusted, depending on desired stiffness; the tighter the hinge-screw, the more accurate the compass's performance. The better quality compass, made of plated metal, is able to be finely adjusted via a small, serrated wheel usually set between the legs (see the "using a compass" animation shown above) and it has a (dangerously powerful) spring encompassing the hinge. This sort of compass is often known as a "pair of Spring-Bow Compasses".

Needle point

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The needle point is located on the steady leg, and serves as the center point of the circle that is about to be drawn.

Pencil lead

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The pencil lead draws the circle on a particular paper or material. Alternatively, an ink nib or attachment with a technical pen may be used. The better quality compass, made of metal, has its piece of pencil lead specially sharpened to a "chisel edge" shape, rather than to a point.

Adjusting nut

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This holds the pencil lead or pen in place.

Uses

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Circles can be made by pushing one leg of the compasses into the paper with the spike, putting the pencil on the paper, and moving the pencil around while keeping the legs at the same angle. Some people who find this action difficult often hold the compasses still and move the paper round instead. The radius of the intended circle can be changed by adjusting the initial angle between the two legs.

Distances can be measured on a map using compasses with two spikes, also called a dividing compass (or just "dividers"). The hinge is set in such a way that the distance between the spikes on the map represents a certain distance in reality, and by measuring how many times the compasses fit between two points on the map the distance between those points can be calculated.

Compasses and straightedge

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Compasses-and-straightedge constructions are used to illustrate principles of plane geometry. Although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles. The most rigorous definition of this abstract tool is the "collapsing compass"; having drawn a circle from a given point with a given radius, it disappears; it cannot simply be moved to another point and used to draw another circle of equal radius (unlike a real pair of compasses). Euclid showed in his second proposition (Book I of the Elements) that such a collapsing compass could be used to transfer a distance, proving that a collapsing compass could do anything a real compass can do.

Variants

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A beam compass is an instrument, with a wooden or brass beam and sliding sockets, cursors or trammels, for drawing and dividing circles larger than those made by a regular pair of compasses.[2]

Scribe-compasses[3] is an instrument used by carpenters and other tradesmen. Some compasses can be used to draw circles, bisect angles and, in this case, to trace a line. It is the compass in the most simple form. Both branches are crimped metal. One branch has a pencil sleeve while the other branch is crimped with a fine point protruding from the end. A wing nut on the hinge serves two purposes: first it tightens the pencil and secondly it locks in the desired distance when the wing nut is turned clockwise.

Loose leg wing dividers[4] are made of all forged steel. The pencil holder, thumb screws, brass pivot and branches are all well built. They are used for scribing circles and stepping off repetitive measurements[5] with some accuracy.

A reduction compass or proportional dividers is used to reduce or enlarge patterns while conserving angles.

Ellipse drawing compasses are used to draw ellipse.

Compass variants

As a symbol

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A computer drawn compass, used to symbolize precise designing of applications.

A pair of compasses is often used as a symbol of precision and discernment. As such it finds a place in logos and symbols such as the Freemasons' Square and Compasses and in various computer icons. English poet John Donne used the compass as a conceit in "A Valediction: Forbidding Mourning" (1611).

  • Compass for tracing a line.
    Compass for tracing a line.
  • Flat branch, pivot wing nut, pencil sleeve branch of the scribe-compass.
    Flat branch, pivot wing nut, pencil sleeve branch of the scribe-compass.
  • 6 inch (15 cm) dividers made from forged steel.
    6 inch (15 cm) dividers made from forged steel.
  • One type of sector.
    One type of sector.
  • A compass on the former National Emblem of East Germany (former German Democratic Republic).
    A compass on the former National Emblem of East Germany (former German Democratic Republic).
  • The compass is a Masonic symbol that appears on jewellery such as this pendant.
    The compass is a Masonic symbol that appears on jewellery such as this pendant.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Compass (drawing tool)

View on Grokipedia
from Grokipedia
A compass, also known as a pair of compasses, is a instrument consisting of two adjustable legs joined by a , with one leg typically ending in a sharp metal point for anchoring on a surface and the other equipped with a , , or for marking circles and arcs of precise radius. This design enables accurate geometric constructions, distance measurements, and the transfer of lengths between drawings, making it indispensable in fields like , , , and drafting. The drawing compass originated in ancient times, with evidence of its use by Greek mathematicians as early as the 3rd century BCE for tracing circles, measuring distances, and performing straightedge-and-compass constructions, as exemplified in Euclid's Elements. By the medieval period in , particularly from the onward, the tool gained symbolic significance as an of divine creation and order, often depicted in religious manuscripts and as held by God to represent architectural and geometric precision in building designs like cathedrals. Over centuries, the compass evolved from simple metal dividers to more sophisticated forms, including bow compasses with spring mechanisms for finer adjustments and beam compasses using an extendable rod for drawing large radii up to several feet. Interchangeable legs for pencils, pens, or points became common by the early , enhancing versatility in technical applications. Today, while software has largely supplanted manual tools in professional settings, the compass endures in educational lessons, artistic endeavors, and specialized trades requiring analog precision.

History

Origins and early development

Evidence of compass use in ancient Egypt dates to the 14th century BCE, as demonstrated by precise geometric constructions in architectural and geometric drawings. A notable artifact is a wooden panel from the tomb of Kha, an architect of the 18th Dynasty (ca. 1400–1350 BCE), featuring an overlapping grid of circles that evidences compass and straightedge constructions, predating similar Greek techniques by centuries. These constructions facilitated the creation of symmetrical designs essential for temple layouts and other architectural works, reflecting advanced practical geometry in Egyptian society. In , around 300 BCE, mathematicians such as referenced compass-like instruments in their work on geometric proofs, integrating them into systematic constructions. Euclid's Elements, particularly Proposition I.9 on angle bisection, describes using a compass to draw intersecting circles from given points, establishing the tool's role in rigorous deductive geometry. This textual evidence underscores the compass's evolution from practical implement to a foundational device in theoretical , influencing subsequent Hellenistic and Roman scholars. The hinged compass design, characterized by riveted legs for adjustable radius, was introduced during the Roman era (ca. 1st century BCE– CE), enhancing portability and precision for drafting and . dividers—early hinged compasses—have been recovered from Roman sites, such as those in the collection, and spread via imperial trade routes across , , and the . These artifacts, often found in workshops and tombs, indicate widespread use among engineers and artisans for mapping and architectural planning. By the 6th century CE, in the , continued to appear in archaeological contexts, as seen in late antique sites like the at Tašačitsa near in Macedonia (4th–5th century CE, extending into early Byzantine phases). A bronze hinged from Grave 31, decorated with motifs like rosettes and herringbone patterns, measures 15.5 cm and exemplifies the tool's persistence in craftsmanship, likely for decorative and structural work. Such finds highlight the 's adaptation in and building projects, bridging ancient traditions into the medieval period.

Evolution in design and materials

During the medieval period (ca. 7th–15th centuries), the hinged design persisted with minimal changes, primarily made of or iron, and was widely used by masons in and the Islamic world for . Traces of compass work appear in Gothic cathedral plans, such as those in the 13th-century portfolio of , where the tool aided in constructing intricate arches and rose windows. The marked a significant advancement in drawing compass design, with instrument makers introducing precision hinges and adjustable mechanisms to enhance accuracy in geometric constructions. English maker Humfrey Cole, active in the late , contributed to this evolution through his work on compendiums that incorporated spaces for drawing tools, reflecting the period's emphasis on refined pivots and scalable arms for architectural and navigational drafting. By the 18th and 19th centuries, materials transitioned from rudimentary wood and bone to more durable brass and steel, allowing for finer control and reduced wear during prolonged use in technical drawing. This shift enabled the development of sturdier joints and interchangeable points, improving the instrument's versatility for both ink and pencil applications. The industrialization of the 19th century further transformed compass production, with companies like Staedtler, founded in 1835, pioneering mass-manufactured steel models that made high-precision tools accessible to educators and professionals. These standardized designs, often featuring brass accents and screw adjustments, supported widespread adoption in schools and engineering workshops. In the , key innovations such as spring-loaded joints simplified adjustments and maintained consistent tension, making compasses more user-friendly for precise small-scale work. This feature, evident in bow and hair-spring variants, built on earlier mechanisms to facilitate quick setups in drafting and design.

Components

Structural features

A standard drawing compass consists of two primary legs connected at a central , forming a V-shaped body that provides the foundational framework for precise circular constructions. The body is typically constructed from durable materials such as metal (often or ) or high-impact to ensure longevity and resistance to wear during repeated use. The , integrated into the upper portion of the body just above the , is ergonomically designed for secure grip, usually measuring about 1.25 cm in length and shaped to fit comfortably between the thumb and . This ridged or cylindrical enhances control and prevents slippage, particularly in extended sessions. The legs themselves are slender extensions from the , generally 4 to 6 inches in total length for standard models, allowing for circles up to 12 inches in when fully extended. A pivot mechanism at the , often featuring a tight head or pin, maintains stability by keeping the legs aligned and resistant to unintended movement during operation. At the , an adjusting nut or enables precise control over the leg separation width, typically employing a fine-threaded mechanism for smooth, incremental adjustments without backlash. This component locks the legs in position once set, contributing to the tool's overall rigidity. Standard models prioritize portability, with overall dimensions compact enough to fit in a geometry kit (around 6 inches long when closed), balancing sturdiness with ease of transport.

Functional elements

The needle point, located at the end of one leg, consists of a sharp metal tip designed to anchor the compass firmly on the drawing surface without slipping, serving as the pivot for creating circles and arcs. This component is typically conical or pointed to minimize surface damage while ensuring stability during rotation. In many models, the needle point is replaceable to address wear from repeated use, allowing users to swap it out for a new one to maintain precision. The pencil lead holder, positioned at the end of the opposite leg, secures a lead for marking the drawing surface as the compass rotates. It features a clamping mechanism, often involving a thumbscrew or split sleeve, to insert and tighten leads of varying hardness, such as HB for general-purpose drawing due to its balanced darkness and durability. This setup permits easy replacement of worn leads, ensuring consistent line quality without interrupting the drawing process. Hinge mechanics at the top of the legs enable smooth, full 360-degree while maintaining tension for a fixed , typically through a riveted or pivoted that allows the legs to spread or contract. Common designs incorporate a knuckle-like for flexibility, combined with a central adjustment or that applies consistent pressure to hold the set distance. This mechanism ensures the radius remains stable during use, preventing unintended shifts. Interchangeability enhances versatility, with the pencil lead holder often designed to accept alternative attachments such as nibs or ruling pens for applications requiring permanent lines. These components can be swapped via universal adapters, allowing the compass to function with technical pens or other marking tools without altering the core structure.

Operation

Basic adjustment and use

To adjust a drawing compass for basic use, begin by loosening the central nut or hinge mechanism at the top of the tool, which allows the two legs to separate or come together freely. Next, use a ruler to measure the desired radius and set the distance between the needle point and the pencil lead accordingly, ensuring the measurement is precise by aligning the legs against the ruler's markings. Once the radius is set, tighten the nut firmly to lock the legs in place, providing stability during operation and preventing slippage. When preparing to draw, mark the center point on the paper with a light dot, then position the needle point of the directly over it, applying just enough downward to anchor it securely without creating an indentation in the surface. Hold the vertically to maintain balance, using your forefinger or thumb to steady the top if needed, while the lead hovers lightly above the paper. To draw the circle, grasp the handle or control knob at the top of the compass and rotate it smoothly in a full 360-degree motion, either or counterclockwise, while applying even, light pressure to the lead to ensure a consistent line. This rotation should be steady and controlled to avoid wobbling, which could distort the circle's shape. For maintaining a consistent throughout the process, work on a non-slip surface such as a mat or clean sheet to prevent the paper from shifting, and avoid readjusting the legs mid-draw unless drawing multiple circles of varying sizes. Additionally, verify the radius setting by re-measuring with the after tightening, as minor shifts can occur during handling.

Techniques for accuracy

To achieve steady when with a , users should hold the instrument with both hands—one stabilizing the top and the other guiding the —to minimize slippage and ensure even motion. Rotating the consistently in one direction, such as , while applying uniform pressure promotes stability and prevents irregular lines. Keeping the vertical to the surface during avoids in the and maintains precision, particularly for arcs or full circles. Preventing errors begins with proper maintenance of the compass components. Sharpening the pencil lead to a fine point using a dedicated lead pointer ensures clean, precise marks; dull leads cause fuzzy lines and inaccurate intersections, so replacement with harder grades like 2H or is recommended for technical work. Similarly, the needle point must be kept sharp and free of bends or rounding to eliminate leg wobble, which can shift the center and enlarge the drawn ; visually inspect or test on scrap to ensure it pierces cleanly without bending, and replace if damaged. Before drawing, jam the needle firmly into the near the intended center to secure it against slippage. Calibration enhances reliability by verifying the set radius. After adjustment, measure the distance between the needle point and pencil tip against a ruler or integrated scale on a drawing board to confirm accuracy, adjusting as needed to match the desired dimension. This step is crucial for repeated constructions, where even minor discrepancies accumulate into significant errors. Different surfaces require adaptations to reduce slippage and . On smooth or uneven , secure the sheet to a using clamping strips to create a taut, stable base that prevents shifting during rotation. The board's non-slip feet and smooth surface further minimize wobble, allowing the needle to hold position reliably without tearing the . Avoid pressing excessively hard on glossy or thin media, as this can cause the needle to skid; instead, rely on the board's for control.

Applications

Everyday and educational uses

In school geometry classes, the drawing compass is commonly employed to create precise circles and arcs for diagrams, enabling students to illustrate concepts such as inscribed figures and cyclic patterns. This hands-on tool facilitates the visualization of basic geometric shapes without relying on digital alternatives, fostering an understanding of manual precision in technical drawing. Beyond formal education, the compass finds practical application in crafts like and , where it aids in drafting curved patterns and templates. For instance, in , it is used to draw smooth curves for garment seams or add seam allowances around pattern edges, ensuring accurate fabric cuts. In , artisans employ the compass to mark out arcs and circles on wood surfaces, such as for layout in or creating symmetrical components like table legs. The educational value of the compass lies in its ability to teach core circle properties through interactive practice, including the as the distance from to edge, the as twice the radius, and the as the perimeter measurement. By adjusting the compass arms to specific lengths and drawing repeated , students gain tactile insight into these relationships, reinforcing mathematical principles in an engaging manner. In art classes, the compass supports the creation of symmetrical designs, particularly mandalas, by allowing artists to draw concentric circles and radial divisions from a central point. This technique promotes exploration of and pattern repetition, blending geometric accuracy with creative expression in projects that emphasize balance and proportion.

Professional and technical applications

In mechanical drawing, the compass plays a crucial role in creating precise arcs and circles essential for blueprints and schematics, allowing draftsmen to represent curved components such as fillets, radii on parts, and structural elements with high accuracy. For instance, in graphics, compasses are employed alongside rulers and protractors to construct geometric shapes that form the basis of technical illustrations for and . In , the drawing facilitates the construction of scale elements, including circular graphic scales and roses, which provide directional orientation and on maps. Traditional mapmakers use the tool to transfer distances and draw concentric circles for projections, ensuring consistent scaling in hand-drafted charts before modern digital methods. Within jewelry design, the enables jewelers to layout precise circular patterns for settings and engravings, such as marking points for prong placements or concentric rings around faceted stones. This precision is vital in creating symmetrical designs, like radial hole patterns on metal sheets for holding pearls or spinels, where even minor deviations could affect fit and . In , the compass integrates seamlessly with tools like the protractor to achieve complex constructions, such as angled arcs in diagrams, by first setting angular measurements and then scribing curves from those points. This combination enhances accuracy in fields like and mechanical , where precise angular and radial elements must align in schematics.

Geometric Role

In compass-straightedge constructions

The compass and constitute the core toolkit for classical in , enabling the creation of geometric figures through a sequence of precise operations without reliance on numerical measurements or coordinates. This method, often termed compass-straightedge , underpins the synthetic approach to geometry where points, lines, and circles are generated iteratively from given elements. The rules governing these constructions are formalized in Euclid's five postulates from The Elements, circa 300 BCE. Postulate 1 permits drawing a straight line from any point to any point using the , while Postulate 2 allows extending a finite straight line continuously in a straight line. Postulate 3 enables the to describe a with any center and radius, limited to arcs or full circles centered at existing points with radii equal to existing line segments. These operations prohibit marking the straightedge or transferring distances arbitrarily, ensuring all constructions remain within the bounds of Euclidean axioms. In this framework, constructible points are those obtainable by intersecting lines and circles derived from an initial set of points, emphasizing geometric intuition over algebraic computation. Historically, 's Elements systematized these tools as the basis for plane geometry, compiling and proving theorems through constructions that avoided coordinate systems or non-Euclidean methods, influencing mathematical pedagogy for over two millennia. This approach highlights constructibility as a key concept, where lengths, angles, and figures must be achievable via finite sequences of the permitted operations, reflecting the emphasis on rigorous, tool-limited deduction. A notable limitation of compass-straightedge constructions is their inability to solve certain classical problems, such as —constructing a square with area equal to a given circle using only these tools. This impossibility was rigorously proven in 1882 by , who demonstrated that π is a , hence not constructible from rational lengths via algebraic extensions of degree powers of 2, as required by the field's properties under these operations.

Key geometric principles and examples

The perpendicular bisector of a AB is constructed by drawing two arcs centered at A and B, each with greater than half the length of AB, such that the arcs intersect at two points; the line connecting these intersection points passes through the of AB and is to it. This method relies on the principle that any point from A and B lies on the perpendicular bisector, as the intersecting arcs ensure equal distances from the endpoints. Similarly, an on segment AB is formed by drawing arcs centered at A and B, each with AB; their intersection point C satisfies AC = AB = BC, completing the triangle ABC. Thales' theorem states that if A and B are the endpoints of a 's and C is any point on the circumference, then angle ACB is a . This can be illustrated with compass and straightedge by constructing a with AB, marking point C on the , and verifying the at C via the subtending the , which measures half the of 180 degrees. Certain regular polygons are constructible with compass and straightedge, such as the regular pentagon, whose side and diagonal lengths are related by the ϕ=1+52\phi = \frac{1 + \sqrt{5}}{2}
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