An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates the following geometric relationship: " t = √(a&sup2 - (R + r)&sup2, a = √(t&sup2 - (R + r)&sup2 "

Model Of Geometric Relationships In 2 Circles

An illustration showing a model of 2 circles with tangent lines, diameters, and radii that illustrates…

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of Circle

Illustration of a sector of a circle. A sector is the space between an arc and two radii drawn to the…

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn to the extremities of the arc.

Sector Of A Hollow Circle

Illustration of a sector of a hollow circle. A sector is the space between an arc and two radii drawn…

The bone contains a multitude of small irregular spaces, approximately fusiform in shape, called lacunae, with very minute canals leading from them and anastomosing with similar little prolongations from the other lacunae. Shown is a transverse section of compact bony tissue of a humerus. Three of the Haversian canals are seen, with their concentric rings; also the lacunae, with the canaliculi were filled with debris in grinding down the section, and therefore appear black in the figure, which represents the object as viewed with transmitted light. The Haversian systems are so closely packed in this section that scarcely any interstitial lamellae are visible.

Microscopic Structure of Bone

The bone contains a multitude of small irregular spaces, approximately fusiform in shape, called lacunae,…

"Morphology of a typical dicotyledonous plant. A, leaf, pinnately-netted veined; B, portion of stem, showing concentric layers of wood; C, ground-plan of flower (the parts in 5's); D, perspective of flower; E, longitudinal section of seed, showing dicotyledonous embryo." -Gager, 1916

Dicotyledonous Morphology

"Morphology of a typical dicotyledonous plant. A, leaf, pinnately-netted veined; B, portion of stem,…

Illustration showing that a circle may be considered as made up of triangles whose bases form the circumference.

Triangles Making Up A Circle

Illustration showing that a circle may be considered as made up of triangles whose bases form the circumference.

In changing the compass from a small to large radius, hold the legs together with one hand and spin the nut with the other, in order to save wear on the threads.

Adjusting the Compass

In changing the compass from a small to large radius, hold the legs together with one hand and spin…

To properly change the compass from one size to another, make sure to place legs together while turning the nut slowly.

Compass Adjustment

To properly change the compass from one size to another, make sure to place legs together while turning…

A compass is a navigational instrument for determining direction relative to the poles.

Turning the Compass

A compass is a navigational instrument for determining direction relative to the poles.

The bow pencil is used to draw small circles and arcs.

The Bow Pencil

The bow pencil is used to draw small circles and arcs.

"They swim rapidly, describing incessantly capricious circles. These movements have gained for them the name of Whirligigs. They have four eyes, the lower ones looking into the water, while the upper eyes look upward toward the air."

Gyrinus Natator

"They swim rapidly, describing incessantly capricious circles. These movements have gained for them…

"They swim rapidly, describing incessantly capricious circles. These movements have gained for them the name of Whirligigs. They have four eyes, the lower ones looking into the water, while the upper eyes look upward toward the air."

Larva of Gyrinus Natator

"They swim rapidly, describing incessantly capricious circles. These movements have gained for them…

Vertical section of a tooth in situ. Labels: c, pulp cavity; 1, enamel with radial and concentric markings; 2, dentin with tubules and incremental lines; 3, cementum or crusta petrosa; 4, pericemental membrane; 5, bone of mandible.

Vertical Section of a Tooth

Vertical section of a tooth in situ. Labels: c, pulp cavity; 1, enamel with radial and concentric markings;…

A lobule of the thymus of a child, as seen under low power. Labels: C, cortex; c, concentric corpuscles within medulla; b, blood vessels; tr, trabeculae.

Lobe of the Thymus

A lobule of the thymus of a child, as seen under low power. Labels: C, cortex; c, concentric corpuscles…

Illustration showing a circle formed by the intersection of a plane perpendicular to the axis of the cone.

Circle

Illustration showing a circle formed by the intersection of a plane perpendicular to the axis of the…

Her Majesty's Royal Palace and Fortress, more commonly known as the Tower of London (and historically as The Tower), is a historic monument in central London, England, on the north bank of the River Thames. The Tower of London is often identified with the White Tower, the original stark square fortress built by William the Conqueror in 1078. However, the tower as a whole is a complex of several buildings set within two concentric rings of defensive walls and a moat. The tower's primary function was a fortress, a royal palace, and a prison (particularly for high status and royal prisoners).

Procession to the Tower of London

Her Majesty's Royal Palace and Fortress, more commonly known as the Tower of London (and historically…

Harlech Castle, located in Harlech, Gwynedd, Wales, is a concentric castle, constructed atop a cliff close to the Irish Sea. Architecturally, it is particularly notable for its massive gatehouse. Built by King Edward I during his conquest of Wales, the castle was subject to several assaults and sieges during its period of active use as a fortification. The seven-year siege of the castle, during the War of the Roses, has been memorialised in the famous song, "Men of Harlech".

Harlech Castle

Harlech Castle, located in Harlech, Gwynedd, Wales, is a concentric castle, constructed atop a cliff…

An illustration depicting the formation of circles of diffusion. "From point A luminous rays enter the eye in the form of a cone, the kind of which will depend on the pupil. Thus it may be circular, or oval, or ever triangular. If the pencil is focused in front of the retina, as at d, or behind it as it as at f, or, in other words, if the retina of being at F; be in the position G or H, there will be a luminous circle or a luminous triangular space, and many elements of the retina will be affected. The size of these diffusion circles depends on the distance from the retina of the point where the rays are focused: the greater the distance, the more extended will be the diffusion circle" (Britannica, 132).

Formation of Circles of Diffusion

An illustration depicting the formation of circles of diffusion. "From point A luminous rays enter the…

The deadbeat has a second face on the pallets, called the 'locking' face, with a curved surface concentric with the pivot that the anchor turns on. When an escape wheel tooth is resting against one of these faces, its force is directed through the pivot axis, so it gives no impulse to the pendulum, allowing it to swing freely. During most of the pendulum's swing, the tooth is in this locked position. Near the bottom of the pendulum's swing the tooth slides off the locking face onto the slanted 'impulse' face of the pallet, allowing the escape wheel to turn and give the pendulum a push, before dropping off the pallet. The drag of the escape tooth on the locking face does add a small amount of friction to the pendulum's swing (this is called a frictional rest type escapement), but it is usually negligible. In contrast to the backward slant of the anchor escape wheel teeth, the deadbeat escape wheel teeth usually slant forward to ensure that the tooth makes contact with the locking face of the pallet, preventing recoil.

Deadbeat Escapement

The deadbeat has a second face on the pallets, called the 'locking' face, with a curved surface concentric…

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically found on the bases of columns and pilasters, or on door and window arches.

Rich Enrichment Bead Moulding

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically…

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically found on the bases of columns and pilasters, or on door and window arches.

Rich Enrichment Bead Moulding

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically…

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically found on the bases of columns and pilasters, or on door and window arches.

Rich Enrichment Bead Moulding

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically…

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically found on the bases of columns and pilasters, or on door and window arches.

Rich Enrichment Bead Moulding

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically…

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically found on the bases of columns and pilasters, or on door and window arches.

Rich Enrichment Bead Moulding

The rich enrichment bead moulding is a Renaissance design of semi-circles. These designs were typically…

Caerphilly Castle is a Norman castle that dominates the centre of the town of Caerphilly in south Wales. Caerphilly Castle was built to stop Llywelyn's southward ambitions. It is the largest castle in Wales, the second largest in Britain (second to Windsor Castle) and is one of the largest fortresses in Europe. Built mainly between 1268 and 1271, it is an early example of a concentric castle.

Caerphilly Castle

Caerphilly Castle is a Norman castle that dominates the centre of the town of Caerphilly in south Wales.…

Roman mosaic pattern of interlocking circles.

Roman Mosaic Circle Pattern

Roman mosaic pattern of interlocking circles.

Illustration used to show how to find the center when given an arc and its radius.

Construction Of Center

Illustration used to show how to find the center when given an arc and its radius.

Illustration used to show how to pass a circumference through any three points not in the same straight line.

Construction Of Circumference

Illustration used to show how to pass a circumference through any three points not in the same straight…

Illustration used to show how to inscribe a square in a given circle.

Construction Of Square Inscribed In Circle

Illustration used to show how to inscribe a square in a given circle.

Illustration used to show how to inscribe a regular hexagon in a given circle.

Construction Of Hexagon Inscribed In Circle

Illustration used to show how to inscribe a regular hexagon in a given circle.

Illustration used to show how to inscribe a regular pentagon in a given circle.

Construction Of Pentagon Inscribed In Circle

Illustration used to show how to inscribe a regular pentagon in a given circle.

Illustration used to show how to inscribe a regular octagon in a given circle.

Construction Of Octagon Inscribed In Circle

Illustration used to show how to inscribe a regular octagon in a given circle.

Illustration used to show how to inscribe any regular polygon in a given circle.

Construction Of Polygon Inscribed In Circle

Illustration used to show how to inscribe any regular polygon in a given circle.

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Construction Of Regular Polygon

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal in length to a given straight line."

Construction Of Arc

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal…

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Construction Of Line Equal To Arc

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Illustration of a circle inside of a rectangle. The two figures have the same center.

Circle Inside Rectangle

Illustration of a circle inside of a rectangle. The two figures have the same center.

Illustration of a circle inside of 2 concentric rectangles whose vertices are connected by line segments.

Circle Inside Concentric Rectangles

Illustration of a circle inside of 2 concentric rectangles whose vertices are connected by line segments.

"Exogen. 1. Section of a branch of three years' growth: a, medulla or pith; b b, medullary sheath; e e, medullary rays; c c c, circles of annual growth; d, bark. 2. Netted veined leaf (oak). 3. Dicotyledonous seed: a, cotyledon. 4. Germination of dicotyledonous seed: a a, seed-leaves or cotyledons; o, plumula. 5. Exogenous flower (crowfoot)." -Whitney, 1911

Section of Branch Showing Exogen

"Exogen. 1. Section of a branch of three years' growth: a, medulla or pith; b b, medullary sheath; e…

"Fake. Naut., one of the circles or windings of a cable or hawser as it lies in a coil; a single turn or coil, as one of the oblong loops into which a shot-line is wound in being placed in a faking-box." -Whitney, 1911

Rope Coiled in Fakes on Deck

"Fake. Naut., one of the circles or windings of a cable or hawser as it lies in a coil; a single turn…

Development of concentric ridges in anticlinal structures. A) An anticlinal or cigar-shaped mountain results from the position of the hard rock. B) The anticlinal mountain A is replaced by an anticlinal valley because of the position of the strata.

Concentric Ridges in Anticlinal Structures

Development of concentric ridges in anticlinal structures. A) An anticlinal or cigar-shaped mountain…

Development of concentric ridges in synclines. A) a region with synclinal or canoe-shaped folds. B) The synclinal valley shown in A is replaced by a mountain because of the occurrence of a hard stratum in the center.

Concentric Ridges in Synclines

Development of concentric ridges in synclines. A) a region with synclinal or canoe-shaped folds. B)…

Illustration of a regular nonagon inscribed in a circle. This could also be described as a circle circumscribed about a regular nonagon.

Nonagon Inscribed in a Circle

Illustration of a regular nonagon inscribed in a circle. This could also be described as a circle circumscribed…

Illustration of a circle inscribed in a regular nonagon. This could also be described as a regular nonagon circumscribed about a circle.

Circle Inscribed in a Nonagon

Illustration of a circle inscribed in a regular nonagon. This could also be described as a regular nonagon…

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Sphere Cut By Plane

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Diagram used to prove the theorem: "All points in the circumference of a circle of a sphere are equally distant from each of its poles."

Circumference of a Circle of a Sphere

Diagram used to prove the theorem: "All points in the circumference of a circle of a sphere are equally…

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Cone depicting Conic Sections

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle, ellipse.

Cone depicting Conic Sections

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle,…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

Illustration used to construct a circle when given three points.

Construction of Circle Given 3 Points

Illustration used to construct a circle when given three points.

Illustration used to draw a tangent to a circle.

Construction of Tangent to a Circle

Illustration used to draw a tangent to a circle.

Illustration used to find the center of a circle.

Center of a Circle

Illustration used to find the center of a circle.

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

Construction of Radii of a Circle

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters equal to the minor and major axes of the ellipse.

Construction of Ellipse by Describing Circles

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters…

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Construction of Ellipse

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

"Argent, a pale azure engrailed. ENGRAILED. Any object being edged with small semi-circles, the points turning outwards, is said to be engrailed." -Hall, 1862

Pale Engrailed

"Argent, a pale azure engrailed. ENGRAILED. Any object being edged with small semi-circles, the points…

"The Young Variable Gordius, after escaping from the egg. c, complete protrusion of both circles of hooklets and the style." -Whitney, 1911

Gordian Worm

"The Young Variable Gordius, after escaping from the egg. c, complete protrusion of both circles of…

Illustration of a circle with radius QR.

Radius of a Circle

Illustration of a circle with radius QR.