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Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Square Inscribed in a 12-Point Star

Illustration of a square inscribed in a closed concave geometric figure with 24 sides in the shape of…

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides in the shape of a 12-point star. The two figures are concentric.

Triangle Inscribed In A 12-Point Star

Illustration of an equilateral triangle inscribed in a closed concave geometric figure with 24 sides…

"b is a glass tube in water and c is a glass tube in mercury. The surface of the water in the tube b is concave, while the surface of the mercury in the tube c is convex." — Hallock, 1905

Capillary Attraction

"b is a glass tube in water and c is a glass tube in mercury. The surface of the water in the tube b…

"The contours of a concave (hollowed out) cone are close together at the center (top), and far apart at the outside (bottom)." — Moss, 1914

Contours of a concave cone

"The contours of a concave (hollowed out) cone are close together at the center (top), and far apart…

"...and the cornea will become too flat, or not suffciently convex, to make the rays of light meet at the proper place, and the image will therefore tend to be formed beyond the retina, instead of before it..." -Comstock 1850

Cornea too Concave on Eye

"...and the cornea will become too flat, or not suffciently convex, to make the rays of light meet at…

"Heat is radiated at C, which is placed at mirror A's focus. Mirror A catches some of the heat and reflects it across to mirror B which focuses the heat on D." —Quackenbos 1859

Reflection of Radiant Heat

"Heat is radiated at C, which is placed at mirror A's focus. Mirror A catches some of the heat and reflects…

Illustration of an irregular concave heptagon.

Irregular Concave Heptagon

Illustration of an irregular concave heptagon.

Illustration of an irregular hexagon. This is also an example of a concave polygon.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon.

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

A concave hornbill perched on a branch, with mountains rising behind it.

Concave Hornbill

A concave hornbill perched on a branch, with mountains rising behind it.

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved and the other plane.(1) Double convex(2) Plano convex(3) Meniscus(4)Double concave(5) Plano concave(6) Concavo concave." -Avery 1895

Lens

"A lens is a transparent body the two refracting surfaces of which are curved, or one of which is curved…

An illustration of the concave of a meniscus.

Concave of Meniscus

An illustration of the concave of a meniscus.

"The foci of concave mirrors may be in front of the mirror, in which case they are real; or they may be behind teh mirror, in which case they are virtual." -Avery 1895

Foci of Concave Mirror

"The foci of concave mirrors may be in front of the mirror, in which case they are real; or they may…

"A concave mirror reflects from a curved surface hollowing in like he inside of an orange." —Quackenbos 1859

Concave Mirror

"A concave mirror reflects from a curved surface hollowing in like he inside of an orange." —Quackenbos…

"The focus of a concave mirror is the point where the rays are brought together by reflection." -Comstock 1850

Focus of a Concave Mirror

"The focus of a concave mirror is the point where the rays are brought together by reflection." -Comstock…

"Parallel rays of light strike the concave mirror. The rays converge at the focus, F, which is halfway between the mirror surface and the center of the sphere that the mirror would form if it were a full sphere." —Quackenbos 1859

Reflection from Concave Mirrors

"Parallel rays of light strike the concave mirror. The rays converge at the focus, F, which is halfway…

"Thus, were the rays falling on the mirror parallel, the focus would be at a' but in consequence of their previous convergency, they are brought together at a less distance than the principal focus." -Comstock 1850

Convergent Rays in a Concave Mirror

"Thus, were the rays falling on the mirror parallel, the focus would be at a' but in consequence of…

"...be made obvious...where the diverging rays 1, 2, 3, 4 form a focus at the point o, whereas, had they been parallel, their focus would have been at a." -Comstock 1850

Divergent Rays in a Concave Mirror

"...be made obvious...where the diverging rays 1, 2, 3, 4 form a focus at the point o, whereas, had…

"The focus of each point chose may be determined by tracing two rays from the point, and locating their real or apparent intersection after reflection by the mirror. The two rays most convenient for this purpose are teh oen that lies along the axis fo the point, and the one that lies parallel to the principal axis of the mirror." -Avery 1895

Concave Mirror with Image and Focus

"The focus of each point chose may be determined by tracing two rays from the point, and locating their…

"When the object is at a distance from the mirror somewhat greater than the center of curvature, as beyond C, the image is real, inverted, smaller than the object, and at a distance from the mirror greater than that of the principle focus and less than that of the center of curvature, as between F and C." -Avery 1895

Image Beyond the Curvature of a Concave Mirror

"When the object is at a distance from the mirror somewhat greater than the center of curvature, as…

"When the concave mirror is large, say six inches in diameter, and eight or ten inches focal distance, it exhibits the human face of enormous bulk, the spectator being frightened at the size and courseness of his own features." -Comstock 1850

Magnified Face in a Concave Mirror

"When the concave mirror is large, say six inches in diameter, and eight or ten inches focal distance,…

"...if the object is placed more remote from the mirror than the principal focus, and between the focus and the centre of the sphere of which the reflector is a part, then the image will appear inverted on the contrary side of the centre, and farter from the mirror than the object; thus, if a lamp be placed obliquely before a concave mirror, its image will be seem inverted in the air, on the contrary side of a perpendicular line through the centre of the mirror." -Comstock 1850

Object Beyond the Focus in a Concave Mirror

"...if the object is placed more remote from the mirror than the principal focus, and between the focus…

"...let us suppose the object a, to be placed before the mirror, and nearer to it than the principal focus. Then the rays proceeding from the extremities of the object without interruption, would continue to diverge in the lines o and n, as seen behind the mirror' but by reflection they are made to diverge less than before, and consequently to make the angle under which the meet more obtuse at the eye b, than it would be if they continued onward to e, where they would have met without reflection. The result therefore, is to render the image h, upon the eye, as much larger than the object a, as the angle at the eye is more obtuse than the angle at e." -Comstock 1850

Object Within the Focus in a Concave Mirror

"...let us suppose the object a, to be placed before the mirror, and nearer to it than the principal…

"Suppose a red hot ball to be placed in the principle focus of the mirror, a, the rays of heat and light proceeding from it will be reflected in the parallel lines 1, 2, 3 etc." -Comstock 1850

Reflection of Heat Using Concave Mirrors

"Suppose a red hot ball to be placed in the principle focus of the mirror, a, the rays of heat and light…

"The spherical aberration of a concave mirror is the deviation of some of the reflected light from the focus, as shown It arises from the curvature of the mirror, and causes an indistinctness or blurring of the image." -Avery 1895

Spherical Aberration of a Concave Mirror

"The spherical aberration of a concave mirror is the deviation of some of the reflected light from the…

"Suppose the tumbler, a, to be filled with water, and placed beyond the principal focus of the concave mirror, and so managed as to be hid from eye c, by the screen b. The lamp by which the tumbler is illuminated must also be placed behind the screen, and near the tumbler, To a person placed at c, the tumbler with its contents will appear incerted at e, and suspended in the air." -Comstock 1850

Deception by Mirrors

"Suppose the tumbler, a, to be filled with water, and placed beyond the principal focus of the concave…

"Concave or Adherent Surface of the Nail. <em>A</em>, border of the root; <em>B</em>, whitish portion of semi-lunar shape; <em>C</em>, body of nail. The continuous line around border represents the free edge." &mdash; Blaisedell, 1904

Surface of a nail

"Concave or Adherent Surface of the Nail. A, border of the root; B, whitish portion…

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Concave Nonagon

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with…

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Concave Nonagon

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with…

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Concave Nonagon

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with…

Illustration of 2 regular congruent nonagons that have the same center. One nonagon has been rotated 20&deg; in relation to the other.

2 Congruent Rotated Nonagons

Illustration of 2 regular congruent nonagons that have the same center. One nonagon has been rotated…

Illustration of an irregular concave octagon. This polygon has some symmetry.

Irregular Concave Octagon

Illustration of an irregular concave octagon. This polygon has some symmetry.

Illustration of an irregular concave octagon.

Irregular Concave Octagon

Illustration of an irregular concave octagon.

Illustration of an irregular concave octagon. This polygon has some symmetry.

Irregular Concave Octagon

Illustration of an irregular concave octagon. This polygon has some symmetry.

Illustration of an irregular concave octagon. This polygon has some symmetry.

Irregular Concave Octagon

Illustration of an irregular concave octagon. This polygon has some symmetry.

Illustration of an irregular pentagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Pentagon

Illustration of an irregular pentagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular concave pentagon.

Irregular Concave Pentagon

Illustration of an irregular concave pentagon.

Illustration of a concave polygon. A concave polygon is a polygon of which tow or more sides, if produced, will enter the polygon.

Concave Polygon

Illustration of a concave polygon. A concave polygon is a polygon of which tow or more sides, if produced,…

"If a pair of concave mirrors be set facing each other, as shown in figure 7, and a source of heat be placed in the focus of one, a thermometer in the focus of the other will quickly show a rise in temperature though the mirrors are many feet apart." Louis Derr, 1911

A Pair of Concave Mirrors Set Facing Each Other

"If a pair of concave mirrors be set facing each other, as shown in figure 7, and a source of heat be…

"Hold a lamp reflector or other large concave mirror directly facing the sun, so as to bring the rays of light to a focus...At some point, W, between F and C, the center of curvature of the reflector, hang a loud-ticking watch, and hunt for the point, X, at which the ear can most distinctly hear the ticking. Moving the reflector will render the sound inaudible." -Avery 1895

Reflection of Sound Using a Reflector

"Hold a lamp reflector or other large concave mirror directly facing the sun, so as to bring the rays…

Illustration of a closed concave geometric figure with 20 sides in the shape of a 10-point star.

10-Point Star

Illustration of a closed concave geometric figure with 20 sides in the shape of a 10-point star.

Illustration of a closed concave geometric figure with 24 sides in the shape of a 12-point star.

12-Point Star

Illustration of a closed concave geometric figure with 24 sides in the shape of a 12-point star.

Illustration of a closed concave geometric figure with 16 sides in the shape of a 8-point star.

8-Point Star

Illustration of a closed concave geometric figure with 16 sides in the shape of a 8-point star.

Illustration of a closed concave geometric figure with 18 sides in the shape of a 9-point star.

9-Point Star

Illustration of a closed concave geometric figure with 18 sides in the shape of a 9-point star.