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Illustration of a square inscribed in a circle. This can also be described as a circle circumscribed about a square. The diagonal of the square is also the diameter of the circle.

Square Inscribed In A Circle

Illustration of a square inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a square, with diagonals drawn, inscribed in a circle. This can also be described as a circle circumscribed about a square. The diagonals, which are also the diameter of the circle, intersect at the center of both the square and the circle.

Square Inscribed In A Circle

Illustration of a square, with diagonals drawn, inscribed in a circle. This can also be described as…

Illustration of a square, with diagonals drawn, circumscribed about a circle. This can also be described as a circle inscribed in a square. The diagonals of the square intersect at the center of both the square and the circle. The diagonals coincide with the diameter of the circle.

Square Circumscribed About A Circle

Illustration of a square, with diagonals drawn, circumscribed about a circle. This can also be described…

Illustration of a square, with 1 diagonals drawn, circumscribed about a circle. This can also be described as a circle inscribed in a square. The diagonal goes through the center of both the square and the circle and coincides with the diameter of the circle.

Square Circumscribed About A Circle

Illustration of a square, with 1 diagonals drawn, circumscribed about a circle. This can also be described…

Illustration of a square circumscribed about a circle. This can also be described as a circle inscribed in a square.

Square Circumscribed About A Circle

Illustration of a square circumscribed about a circle. This can also be described as a circle inscribed…

Illustration of a regular pentagon inscribed in a circle. This can also be described as a circle circumscribed about a regular pentagon.

Regular Pentagon Inscribed In A Circle

Illustration of a regular pentagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular pentagon circumscribed about a circle. This can also be described as a circle inscribed in a regular pentagon.

Regular Pentagon Circumscribed About A Circle

Illustration of a regular pentagon circumscribed about a circle. This can also be described as a circle…

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed about a regular hexagon.

Regular Hexagon Inscribed In A Circle

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed about a regular hexagon. All diagonals of the hexagon are also diameters of the circle. The diagonals intersect at the center of both the hexagon and the circle.

Regular Hexagon Inscribed In A Circle

Illustration of a regular hexagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular hexagon circumscribed about a circle. This can also be described as a circle inscribed in a regular hexagon.

Regular Hexagon Circumscribed About A Circle

Illustration of a regular hexagon circumscribed about a circle. This can also be described as a circle…

Illustration of a regular heptagon/septagon inscribed in a circle. This can also be described as a circle circumscribed about a regular heptagon/septagon.

Regular Heptagon/Septagon Inscribed In A Circle

Illustration of a regular heptagon/septagon inscribed in a circle. This can also be described as a circle…

Illustration of a regular heptagon/septagon circumscribed about a circle. This can also be described as a circle inscribed in a regular heptagon/septagon.

Regular Heptagon/Septagon Circumscribed about a Circle

Illustration of a regular heptagon/septagon circumscribed about a circle. This can also be described…

Illustration of a regular octagon inscribed in a circle. This can also be described as a circle circumscribed about a regular octagon.

Regular Octagon Inscribed In A Circle

Illustration of a regular octagon inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a regular octagon circumscribed about a circle. This can also be described as a circle inscribed in a regular octagon.

Regular Octagon Circumscribed About A Circle

Illustration of a regular octagon circumscribed about a circle. This can also be described as a circle…

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

Regular Nonagon Inscribed In A Circle

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

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

Regular Nonagon Circumscribed About A Circle

Illustration of a regular nonagon circumscribed about a circle. This can also be described as a circle…

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a circle circumscribed about a pentagon. In this illustration, the pentagon is not regular (the lengths of the sides are not equal).

Cyclic Pentagon

Illustration of a cyclic pentagon, a pentagon inscribed in a circle. This can also be described as a…

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described as a circle circumscribed about a quadrilateral. In this illustration, the quadrilateral is not regular (the lengths of the sides are not equal).

Cyclic Quadrilateral

Illustration of a cyclic quadrilateral, a quadrilateral inscribed in a circle. This can also be described…

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle circumscribed about a hexagon. In this illustration, the hexagon is not regular (the lengths of the sides are not equal).

Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle circumscribed about a hexagon. In this illustration, the hexagon is not regular (the lengths of the sides are not equal).

Cyclic Hexagon

Illustration of a cyclic hexagon, a hexagon inscribed in a circle. This can also be described as a circle…

Illustration of a hexagon in a circle. Four of the six vertices of the hexagon are bound by the circle (are tangent to the circle). Because all six vertices are not on the circle, the hexagon is not cyclic; it is not inscribed in the circle.

Hexagon In A Circle

Illustration of a hexagon in a circle. Four of the six vertices of the hexagon are bound by the circle…

Illustration of a 5-point star inscribed in a circle. This can also be described as a circle circumscribed about a 5-point star.

Star Inscribed In A Circle

Illustration of a 5-point star inscribed in a circle. This can also be described as a circle circumscribed…

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of David) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or two triangles.

Star Inscribed In A Circle

Illustration of a 6-point star created by two equilateral triangles (often described as the Star of…

Illustration of a 6-point star (convex dodecagon) inscribed in a circle. This can also be described as a circle circumscribed about a 6-point star, or convex dodecagon.

Star Inscribed In A Circle

Illustration of a 6-point star (convex dodecagon) inscribed in a circle. This can also be described…

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of a 6-point star (convex dodecagon) inscribed in a large circle and circumscribed about…

Illustration of a 6-point star (convex dodecagon) circumscribed about a circle. This can also be described as a circle inscribed in a 6-point star, or convex dodecagon.

Star Circumscribed About A Circle

Illustration of a 6-point star (convex dodecagon) circumscribed about a circle. This can also be described…

Illustration of an 8-point star, created by two squares at 45° rotations, inscribed in a circle. This can also be described as a circle circumscribed about an 8-point star, or two squares.

Star Inscribed In A Circle

Illustration of an 8-point star, created by two squares at 45° rotations, inscribed in a circle.…

Illustration of an 8-point star, or convex polygon, inscribed in a circle. This can also be described as a circle circumscribed about an 8-point star.

Star Inscribed In A Circle

Illustration of an 8-point star, or convex polygon, inscribed in a circle. This can also be described…

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about a smaller circle.

Star Inscribed And Circumscribed About Circles

Illustration of an 8-point star (convex polygon) inscribed in a large circle and circumscribed about…

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described as a circle inscribed in an 8-point star, or convex polygon.

Star Circumscribed About A Circle

Illustration of an 8-point star (convex polygon) circumscribed about a circle. This can also be described…

Leaves - simple; alternate; edge lobed (lobes entire). Outline - rounded. Apex - cut almost squarely across, with a shallow hollow, giving a square look to the upper half of the leaf. Base - usually heart-shape. Leaf - three to five inches long and wide; very smooth; with four to six lobes (two lobes at the summit; at the sides two, or two large and two small). Bark - of trunk, dark ash-color and slightly rough. Flowers - four to six inches across, greenish-yellow, marked within with orange, somewhat tulip-like, fragrant solitary. May, June. Found - from Southwestern Vermont to Michigan, southward and westward. Its finest growth is in the valley of the lower Wabash River and along the western slopes of the Alleghany Mountains. General Information - Among the largest and most valuable of the North American Trees. It is usually seventy to one hundred feet high, often much higher, with a straight, clear trunk, that divides rather abruptly at the summit into coarse and straggling branches. The wood is light and soft, straight grained, and easily worked, with the heart wood light yellow or brown, and the thin sap wood nearly white. It is very widely and variously used - for construction, for interior finish, for shingles, in boat-building, for the panels of carriages, especially in the making of wooden pumps and wooden ware of different kings. I asked a carpenter: "Hope, is n't it the tulip wood (which you call poplar*) that the carriage-makers use for their panels?" "Yes, and the reason is, because it shapes so easily. If you take a panel and wet one side, and hold the other side to a hot stove-pipe, the piece will just hub the pipe. It's the best wood there is for panelling." "Of all the trees of North America with deciduous leaves, the tulip tree, next to the buttonwood, attains the amplest dimensions, while the perfect straightness and uniform diameter of its trunk for upwards of forty feet, the more regular disposition of its branches, and the greater richness of its foliage, give it a decided superiority over the buttonwood and entitle it to be considered as one of the most magnificent vegetables of the temperate zone." - Michaux. *The name should be dropped. The tree is not a poplar. The tulip tree was very highly esteemed by the ancients; so much so that in some of their festivals they are said to have honored it by pouring over its roots libations of wine.

Genus Liriodendron, L. (Tulip Tree)

Leaves - simple; alternate; edge lobed (lobes entire). Outline - rounded. Apex - cut almost squarely…

An erasing shield of thin metal is convenient in erasing desired shapes.

Straight Line Erasing Shield

An erasing shield of thin metal is convenient in erasing desired shapes.

This erasing shield can erase multiple sizes and shapes.

Oval Erasing Shield

This erasing shield can erase multiple sizes and shapes.

The various types of oak leaves: "a. Bur oak, b. Live oak, c. Willow oak, d. White oak." -Foster, 1921

Oak Leaves

The various types of oak leaves: "a. Bur oak, b. Live oak, c. Willow oak, d. White oak." -Foster, 1921

Distortions of fossils from uplifting: 1) natural form of the shell Spirifer disjunctus (1-4), 2) shortened one-half, 3) shortened above the middle and lengthened below it, 4) upper pressed, lower drawn out, 5) like 3, 6) similar cleavage-plane, 7) lower part prolonged, 8) natural form of Spirifer giganteus (5-8).

Distortion of Fossils

Distortions of fossils from uplifting: 1) natural form of the shell Spirifer disjunctus (1-4), 2) shortened…

"The (010) plane of an orthoclase crystal." -Johannsen, 1908

Orthoclase Crystal

"The (010) plane of an orthoclase crystal." -Johannsen, 1908

"The (001) plane of an orthoclase crystal." -Johannsen, 1908

Orthoclase Crystal

"The (001) plane of an orthoclase crystal." -Johannsen, 1908

A simple orthoclase crystal.

Orthoclase Crystal

A simple orthoclase crystal.

A simple orthoclase crystal.

Orthoclase Crystal

A simple orthoclase crystal.

A simple orthoclase crystal.

Orthoclase Crystal

A simple orthoclase crystal.

"Simple orthoclase crystal showing cleavage lines and the position of the twinning plane in a Carlsbad twin." -Johannsen, 1908

Orthoclase Crystal

"Simple orthoclase crystal showing cleavage lines and the position of the twinning plane in a Carlsbad…

"Simple orthoclase crystal opened out to show the optical orientation." -Johannsen, 1908

Orthoclase Crystal

"Simple orthoclase crystal opened out to show the optical orientation." -Johannsen, 1908

"A Carlsbad twin of orthoclase." -Johannsen, 1908

Orthoclase Twin

"A Carlsbad twin of orthoclase." -Johannsen, 1908

"A Baveno twin of orthoclase." -Johannsen, 1908

Orthoclase Twin

"A Baveno twin of orthoclase." -Johannsen, 1908

"Albite and Carlsbad twinning combined." -Johannsen, 1908

Twinning

"Albite and Carlsbad twinning combined." -Johannsen, 1908

"Positive and negative extinction angles in the feldspars." -Johannsen, 1908

Extinction Angles

"Positive and negative extinction angles in the feldspars." -Johannsen, 1908

"Extinction angles on the (001) faces of the lime-soda feldspars." -Johannsen, 1908

Extinction Angles

"Extinction angles on the (001) faces of the lime-soda feldspars." -Johannsen, 1908

"Extinction angles on the (010) faces of the lime-soda feldspars." -Johannsen, 1908

Extinction Angles

"Extinction angles on the (010) faces of the lime-soda feldspars." -Johannsen, 1908

"A (010) cleavage flake of plagioclase." -Johannsen, 1908

Plagioclase

"A (010) cleavage flake of plagioclase." -Johannsen, 1908

"The (010) face of a Carlsbad twin of plagioclase." -Johannsen, 1908

Plagioclase Twin

"The (010) face of a Carlsbad twin of plagioclase." -Johannsen, 1908

"Development of eel. Change from Leptocephalus shape (I.) to "Elver" shape (V.)." -Thomson, 1916

Eel Development

"Development of eel. Change from Leptocephalus shape (I.) to "Elver" shape (V.)." -Thomson, 1916

An illustration of a circle inscribed in a square. It can be used to show that the area of a circle is .7854 of the area of a square whose sides are equal to its diameter.

Circle Inscribed In A Square

An illustration of a circle inscribed in a square. It can be used to show that the area of a circle…

A perfoliate leaf is when there is a stem through the leaf.

Perfoliate Leaf

A perfoliate leaf is when there is a stem through the leaf.

A clasping leaf around a stem.

Clasping Leaf

A clasping leaf around a stem.

"Anceps.--Two-edged." -Newman, 1850

Anceps

"Anceps.--Two-edged." -Newman, 1850

"Infundibuliformis.--Funnel form." -Newman, 1850

Infundibuliformis

"Infundibuliformis.--Funnel form." -Newman, 1850

A creeping stem.

Creeping Stem

A creeping stem.

A leaf pouch.

Pouch

A leaf pouch.

A square stem.

Square Stem

A square stem.

"Decurrent.--When leaves run down the stem to a point considerably below the place where they diverge from it." -Newman, 1850

Decurrent Leaf

"Decurrent.--When leaves run down the stem to a point considerably below the place where they diverge…