Illustration of a semicircle.

Semicircle

Illustration of a semicircle.

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an axis.

Sphere Made by Revolution of Semicircle

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an…

Illustration of a semicircle with chords and radii.

Semicircle With Chords and Radii

Illustration of a semicircle with chords and radii.

Quarter Eagle ($2.50) United States coin from 1796. Obverse has a right-facing image of Liberty wearing a triangular cap. Reverse shows an heraldic eagle with U.S. shield holding a bundle of arrows and an olive branch in its talons.

Gold Quarter Eagle Coin, 1796

Quarter Eagle ($2.50) United States coin from 1796. Obverse has a right-facing image of Liberty wearing…

Quarter Eagle ($2.50) United States coin from 1803. Obverse has a right-facing image of Liberty wearing a turban-shaped cap surrounded by 13 equally-spaced stars. Reverse shows an eagle with U.S. shield holding a bundle of arrows in its right talon and an olive branch in its left.

Gold Quarter Eagle Coin, 1803

Quarter Eagle ($2.50) United States coin from 1803. Obverse has a right-facing image of Liberty wearing…

Half Eagle ($5.00) United States coin from 1795. Obverse has a right-facing image of Liberty wearing a cap with LIBERTY inscribed above head. Reverse shows an eagle on olive branch in a plain field holding a laurel wreath in its beak with its head turned to the right.

Gold Half Eagle Coin, 1795

Half Eagle ($5.00) United States coin from 1795. Obverse has a right-facing image of Liberty wearing…

Half Eagle ($5.00) United States coin from 1807. Obverse has a left-facing image of Liberty wearing a turban-shaped cap with 13 stars - 7 facing. Reverse shows an eagle and shield with the eagle holding arrows in its left talon and an olive branch in it right. E PLURIBUS UNUM on a banner above the eagle.

Gold Half Eagle Coin, 1807

Half Eagle ($5.00) United States coin from 1807. Obverse has a left-facing image of Liberty wearing…

Eagle ($10.00) United States coin from 1795. Obverse has a right-facing image of Liberty wearing a cap with LIBERTY inscribed above, fifteen stars - 5 facing. Reverse shows an eagle on an olive branch, holding an olive wreath in its beak. Inscription surrounding figure - UNITED STATES OF AMERICA.

Gold Eagle Coin, 1795

Eagle ($10.00) United States coin from 1795. Obverse has a right-facing image of Liberty wearing a cap…

Eagle ($10.00) United States coin from 1838. Obverse has a left-facing image of Liberty wearing a coronet inscribed with LIBERTY and is surrounded by 13 equally-spaced stars. Reverse shows an eagle with shield, without motto, holding a bundle of arrows and an olive branch in its talons, inscription surrounding image - UNITED STATES OF AMERICA.

Gold Eagle Coin, 1838

Eagle ($10.00) United States coin from 1838. Obverse has a left-facing image of Liberty wearing a coronet…

Double Eagle ($20.00) United States coin from 1849. Obverse has a left-facing image of Liberty wearing a coronet inscribed with LIBERTY and is surrounded by 13 equally-spaced stars. Reverse shows an heraldic eagle holding arrows its left talon and an olive branch in it right. Within the ornamental scroll is inscribed E PLURIBUS UNUM and above the image is a circle of 13 stars and rays, inscription surrounding image - UNITED STATES OF AMERICA TWENTY D.

Gold Double Eagle Coin, 1849

Double Eagle ($20.00) United States coin from 1849. Obverse has a left-facing image of Liberty wearing…

Kentucky Issue (unknown) Kentucky State coin from 1796. Obverse has a seated female with a staff and shield and is inscribed around the figure PAYABLE BY P.P.P. MYDDLETON. Reverse shows a group of 4 figures in a field. The inscription which surrounds the image - BRITISH SETTLEMENT KENTUCKY 1796

Silver Kentucky Issue Coin, 1796

Kentucky Issue (unknown) Kentucky State coin from 1796. Obverse has a seated female with a staff and…

Maryland XII Pence (XII Pence) Maryland Colony coin from 1659. Obverse has an image of Lord Baltimore surrounded by the inscription - +CAECILIVS:DNS:TERRAE-MARIAE:&CT;. The reverse shows the Baltimore family shield, the denomination in roman numerals to either side of the shield. The inscription surrounding the image - CRESCITE:ET:MVLTIPLICAMINI. This coin was also struck in copper.

Silver Maryland XII Pence Coin, 1659

Maryland XII Pence (XII Pence) Maryland Colony coin from 1659. Obverse has an image of Lord Baltimore…

Massachusetts XII Pence (XII Pence) Massachusetts Colony coin from 1652. Obverse has an image of a pine tree. The inscription - IN MASATHUSETS. Reverse shows value in Roman Numerals and the year surrounded by the inscription - AN DOM NEW ENGLAND

Silver Massachusetts XII Pence Coin, 1652

Massachusetts XII Pence (XII Pence) Massachusetts Colony coin from 1652. Obverse has an image of a pine…

New Jersey Halfpenny (Halfpenny) New Jersey Colony coin from 1681. Obverse has an image of St. Patrick with staff. The inscription - QUIESCAT PLEBS. Reverse shows the royal harpist and the inscription - FLOREAT REX

Silver New Jersey Halfpenny Coin, 1681

New Jersey Halfpenny (Halfpenny) New Jersey Colony coin from 1681. Obverse has an image of St. Patrick…

Virginia Shilling (Shilling) Virginia Colony coin from 1774. Obverse has an image of a right-facing head with the inscription - GEORGIUS III DEI GRATIA. Reverse shows an image of a crowned coat of arms with the date at the top and the inscription - VIRGI NIA

Silver Virginia Shilling Coin, 1774

Virginia Shilling (Shilling) Virginia Colony coin from 1774. Obverse has an image of a right-facing…

Fugio (unknown) United States coin from 1787. Obverse has the image of a sundial with the inscription - FUGIO 1787 and MIND YOUR BUSINESS. Reverse shows a chain with thirteen links. In the center of the chain is inscribed WE ARE ONE surrounded by UNITED STATES.

Silver Fugio Coin, 1787

Fugio (unknown) United States coin from 1787. Obverse has the image of a sundial with the inscription…

Trime (3 cents) United States coin from 1851. Obverse has the Union shield lying on top of a six-pointed star and is inscribed with - UNITED STATES OF AMERICA with the date at the bottom. Reverse shows by a large, scrolled letter C enclosing the Roman numeral III (denoting value). This image is surrounded 13 equally-spaced stars.

Silver Trime Coin, 1851

Trime (3 cents) United States coin from 1851. Obverse has the Union shield lying on top of a six-pointed…

Dime (10 cents) United States coin from 1796. Obverse has the image of a right-facing Liberty with LIBERTY inscribed above and 1796 inscribed below, surrounded by 13 stars - 6 facing. Reverse shows an heraldic eagle with a left-facing head, banner in beak inscribed with E PLURIBUS UNUM, clouds above.

Silver Dime Coin, 1796

Dime (10 cents) United States coin from 1796. Obverse has the image of a right-facing Liberty with LIBERTY…

Fifth Dollar (20 cents) United States Coin from 1857. Obverse has the image of Liberty beside a shield holding a staff with a cap in her left hand and surrounded by 13 equally-spaced stars. Reverse is an eagle with NO shield with head right-facing surrounded by the inscription - UNITED STATES OF AMERICA TWENTY CENTS.

Silver Fifth Dollar Coin, 1875

Fifth Dollar (20 cents) United States Coin from 1857. Obverse has the image of Liberty beside a shield…

Quarter (25 cents) United States coin from 1796. Obverse has the image of a right-facing Liberty with LIBERTY inscribed above and 1796 inscribed below, surrounded by 13 stars - 6 facing. Reverse shows an heraldic eagle within a wreath surrounded by the inscription - UNITED STATES OF AMERICA.

Silver Quarter Coin, 1796

Quarter (25 cents) United States coin from 1796. Obverse has the image of a right-facing Liberty with…

Quarter (25 cents) United States coin from 1853. Obverse has the image of a Liberty seated beside a shield, holding a staff with a cap in her left hand surrounded by 13 stars and the date at the bottom. Reverse shows an eagle with a left-turned head, holding arrows and an olive branch with rays over its head surrounded by the inscription - UNITED STATES OF AMERICA QUAR. DOL.

Silver Quarter Coin, 1853

Quarter (25 cents) United States coin from 1853. Obverse has the image of a Liberty seated beside a…

Half Dollar (50 cents) United States coin from 1853. Obverse has the image of a Liberty seated beside a shield, holding a staff with a cap in her left hand surrounded by 13 stars and with arrowheads at the date below the image. Reverse shows an eagle with a left-turned head, holding arrows and an olive branch with rays over its head surrounded by the inscription - UNITED STATES OF AMERICA HALF DOL.

Silver Half Dollar Coin, 1853

Half Dollar (50 cents) United States coin from 1853. Obverse has the image of a Liberty seated beside…

Pence (1 pence) Rosa Americana Series coin. Obverse has a right-facing image of George I surrounded by the inscription - GEORGIUS D:G:M BRI FRA ET HIB REX. Reverse shows the letter I between branches, surrounded by an indecipherable Latin inscription.

Copper Pence Coin, No Date

Pence (1 pence) Rosa Americana Series coin. Obverse has a right-facing image of George I surrounded…

Pence (1 pence) Rosa Americana Series coin from 1722. Obverse has a right-facing image of George I surrounded by the inscription - GEORGIUS DEI GRATIA REX. Reverse shows an uncrowned rose surrounded by the inscription - 1722 ROSE AMERICANA UTILE DULCI.

Copper Pence Coin, 1722

Pence (1 pence) Rosa Americana Series coin from 1722. Obverse has a right-facing image of George I surrounded…

Half Pence (1/2 pence) Obverse has the image of an elephant. Obverse has a right-facing image of George I surrounded by the inscription - GEORGIUS DEI GRATIA REX. Reverse shows a harpist surrounded by the inscription - HIBERNIA 1722. This coin was refused in Ireland and set to America.

Copper Half Pence Coin, 1722

Half Pence (1/2 pence) Obverse has the image of an elephant. Obverse has a right-facing image of George…

Miscellaneous coin (unknown) Obverse left-facing image of King George surrounded by the inscription - NO STAMPS THE RESTORE OF COMMERCE 1766. Reverse shows the image of a ship and the word America surrounded by the inscription - THANKS TO THE FRIENDS OF LIBERTY AND TRADE. The last two originally issued in Dublin.

Copper George III Coin, 1766

Miscellaneous coin (unknown) Obverse left-facing image of King George surrounded by the inscription…

Fugio (1 cent) United States coin from 1787. Obverse has the image of a sundial with the inscription - FUGIO 1787 and MIND YOUR BUSINESS. Reverse shows a chain with thirteen links. In the center of the chain is inscribed WE ARE ONE surrounded by UNITED STATES.

Copper Fugio Coin, 1787

Fugio (1 cent) United States coin from 1787. Obverse has the image of a sundial with the inscription…

Half Pence (1/2 pence) Obverse has the image of an elephant. Reverse bears the inscription - GOD: PRESERVE: CAROLINA: AND THE: LORDS: PROPRIETORS 1694

Copper Half Pence Coin, 1695

Half Pence (1/2 pence) Obverse has the image of an elephant. Reverse bears the inscription - GOD: PRESERVE:…

Cent (1 cent) Obverse has the image of a right facing sailing ship. Reverse shows a shield surrounded by 13 equally-spaced stars. Sometimes referred to as the "Carolina Piece"; reason unknown.

Copper Cent Coin, 1659

Cent (1 cent) Obverse has the image of a right facing sailing ship. Reverse shows a shield surrounded…

New Jersey Quarter Pence (quarter pence) New Jersey Colony coin from 1681. One side has an image of St. Patrick with staff under the inscription - QUIESCAT PLEBS. The other side shows the royal harpist and the inscription - FLOREAT REX

Copper Quarter Pence Coin, 1681

New Jersey Quarter Pence (quarter pence) New Jersey Colony coin from 1681. One side has an image of…

New York Cent (1 cent) New York coin from 1787. Obverse has the right-facing image of a man surrounded with the inscription - GEORGE CLINTON. The reverse shows the state coat of arms with the inscription - 1787 EXCELSIOR below the figure.

Copper Cent Coin, 1787

New York Cent (1 cent) New York coin from 1787. Obverse has the right-facing image of a man surrounded…

Pennsylvania Cent (1 cent) Pennsylvania coin from 1785. Obverse has a right-facing image of a head surrounded by the inscription - VERMON AUCTORI. Reverse shows a right-facing image holding scales and a staff surrounded by the inscription - IMMUNE COLUMBIA 1785. No legal coinage.

Copper Cent Coin, 1785

Pennsylvania Cent (1 cent) Pennsylvania coin from 1785. Obverse has a right-facing image of a head surrounded…

Virginia Half Pence (half pence) Virginia Colony coin from 1773. Obverse has an image of a right-facing head with the inscription - GEORGIUS III REX. Reverse shows an image of a crowned coat of arms with the date at the top and the inscription - VIRGI NIA 1773.

Copper Half Pence Coin, 1773

Virginia Half Pence (half pence) Virginia Colony coin from 1773. Obverse has an image of a right-facing…

Washington Cent (1 cent) US coin from 1783. Obverse has an image of a left-facing George Washington surrounded by the inscription - WASHING & INDEPENDENCE 1783. Reverse shows ONE CENT in the center of a wreath surrounded by the inscription UNITED STATES OF AMERICA 1/100.

Copper Cent Coin, 1783

Washington Cent (1 cent) US coin from 1783. Obverse has an image of a left-facing George Washington…

Hard Times Token (unknown) US coin. Obverse has a right-facing image of Andrew Jackson with the inscription - ANDREW JACKSON. Reverse had in the center THE UNION MUST AND SHALL BE PRESERVED, surrounded by branches and encircled by the inscription THE BANK MUST PERISH.

Copper Hard Times Token, ND

Hard Times Token (unknown) US coin. Obverse has a right-facing image of Andrew Jackson with the inscription…

Hard Times Token (unknown) US coin from 1834.. Obverse has a left-facing image of Andrew Jackson holding a sword and money bags, surrounded by the inscription - A PLAIN SYSTEM VOID OF POMP. Reverse shows the image of a balking mule and is inscribed with - THE CONSTITUTION AS I UNDERSTAND IT ROMAN FIRMNESS LL.D. 1834

Copper Hard Times Token, 1834

Hard Times Token (unknown) US coin from 1834.. Obverse has a left-facing image of Andrew Jackson holding…

Hard Times Token (unknown) US coin. Obverse has an image of the front of the Merchants Exchange surrounded by the inscription - MERCHANTS EXCHANGE WALL ST N YORK BUILT 1827 BURNT 1835. Reverse shows the center inscription - NOT ONE CENT FOR TRIBUTE surrounded by a wreath with 9 berries - 3 outside and 6 inside the wreath with a surrounding inscription - MILLIONS FOR DEFENCE.

Copper Hard Times Token, ND

Hard Times Token (unknown) US coin. Obverse has an image of the front of the Merchants Exchange surrounded…

Hard Times Token (unknown) US coin from 1837. Obverse has a tortoise carrying a chest marked SUB TREASURY.  The inscription beneath the turtle reads - 1837 FISCAL AGENT. The surrounding inscription reads EXECUTIVE EXPERIMENT. Reverse shows the left-facing image of a mule surrounded by the inscription - I FOLLOW IN THE STEPS OF MY ILLUSTRIOUS PREDECESSOR.

Copper Hard Times Token, 1837

Hard Times Token (unknown) US coin from 1837. Obverse has a tortoise carrying a chest marked SUB TREASURY.…

Hard Times Token (unknown) US coin from 1841. Obverse has the image of a right-facing sailing ship surrounded by the inscription - WEBSTER CREDIT CURRENT 1841. Reverse shows the center inscription - NOT ONE CENT FOR TRIBUTE surrounded by a wreath with 9 berries - 3 outside and 6 inside the wreath with a surrounding inscription - MILLIONS FOR DEFENCE.

Copper Hard Times Token, 1841

Hard Times Token (unknown) US coin from 1841. Obverse has the image of a right-facing sailing ship surrounded…

Five Shillings Bill (5 shillings) Connecticut currency from 1776. Image of three fruit trees with the banner below the trees inscribed QUI TRA SUS and the inscription surrounding the whole - CONNECTICENSIS SIGILLUS COLONIE

Paper Money, Five Shillings, 1776

Five Shillings Bill (5 shillings) Connecticut currency from 1776. Image of three fruit trees with the…

Six Shillings Bill (6 shillings) Delaware currency from 1777. Image of a left facing sailing ship with a soldier on the left and a farmer on the right.

Paper Money, Six Shillings Bill, 1777

Six Shillings Bill (6 shillings) Delaware currency from 1777. Image of a left facing sailing ship with…

Ten Dollar Bill ($10) Georgia currency from 1776. Image of a palm tree and a stone. Type set with three varieties of borders to each, printed in black and red and copperplate vignettes in various colors.

Paper Money, Ten Dollars Bill, 1776

Ten Dollar Bill ($10) Georgia currency from 1776. Image of a palm tree and a stone. Type set with three…

Two Thirds of a Dollar (2/3 dollar) Maryland currency from 1774. Image on the right shows a shield with a farmer on the left and a fisherman on the right.

Paper Money, Two Thirds of a Dollar Bill, 1774

Two Thirds of a Dollar (2/3 dollar) Maryland currency from 1774. Image on the right shows a shield with…

One Ninth of a Dollar (1/9 dollar) Maryland currency from 1775. No image on bill.

Paper Money, One Ninth of a Dollar Bill, 1775

One Ninth of a Dollar (1/9 dollar) Maryland currency from 1775. No image on bill.

Thirty-Six Shillings (36 shillings) Massachusetts currency from 1775. Image in lower left of an anchored left-facing sailing ship.

Paper Money, Thirty-Six Shillings Bill, 1775

Thirty-Six Shillings (36 shillings) Massachusetts currency from 1775. Image in lower left of an anchored…

Three Dollar ($3) Massachusetts currency from 1780. No image on obverse. Reverse shows the inscription - GUARANTEED BY THE UNITED STATES.

Paper Money, Three Dollar Bill, 1780

Three Dollar ($3) Massachusetts currency from 1780. No image on obverse. Reverse shows the inscription…

Six Pence (6 pence) New Hampshire currency from 1742. Image is the Coat of Arms of Great Britain; large bill.

Paper Money, Six Pence Bill, 1742

Six Pence (6 pence) New Hampshire currency from 1742. Image is the Coat of Arms of Great Britain; large…

One Shilling (1 shilling) New Jersey currency from 1776. Image is the Coat of Arms of Great Britain.

Paper Money, One Shilling Bill, 1776

One Shilling (1 shilling) New Jersey currency from 1776. Image is the Coat of Arms of Great Britain.

One Shilling and Six Pence (1 shilling 6 pence) (18 pence) New Jersey currency from 1781. Image is the Coat of Arms of New Jersey.

Paper Money, One Shilling and Six Pence Bill, 1781

One Shilling and Six Pence (1 shilling 6 pence) (18 pence) New Jersey currency from 1781. Image is the…

Five Pounds (5 pounds) New York currency from 1759. Image is the New York City Coat of Arms. Beneath the image is the inscription - 'TIS DEATH TO COUNTERFEIT THIS BILL.

Paper Money, Five Pounds Bill, 1759

Five Pounds (5 pounds) New York currency from 1759. Image is the New York City Coat of Arms. Beneath…

Five Pounds (5 pounds) New York currency from 1771. Image is the Coat of Arms of New York City. Beneath the image is the inscription - 'TIS DEATH TO COUNTERFEIT THIS BILL.

Paper Money, Five Pounds Bill, 1771

Five Pounds (5 pounds) New York currency from 1771. Image is the Coat of Arms of New York City. Beneath…

Half Dollar (50 cents) New York currency from 1775. Image is the Coat of Arms of New York City.

Paper Money, Half Dollar Bill, 1775

Half Dollar (50 cents) New York currency from 1775. Image is the Coat of Arms of New York City.

Twenty Shillings Bill (20 shillings) Pennsylvania currency from 1756. Image is the Coat of Arms of William Penn. Bill was printed by Benjamin Franklin.

Paper Money, Twenty Shillings Bill, 1756

Twenty Shillings Bill (20 shillings) Pennsylvania currency from 1756. Image is the Coat of Arms of William…

Nine Pence (9 pence) Rhode Island currency from 1786. Image shows an anchor surrounded by the inscription - DOMINE SPERAMUS IN TE

Paper Money, Nine Pence Bill, 1786

Nine Pence (9 pence) Rhode Island currency from 1786. Image shows an anchor surrounded by the inscription…

Five Dollars ($5) South Carolina currency from 1776. Image of a horse surrounded by the inscription - DOMINUM GENEROSA RECUSAT. Wood engraving, rough brown paper.

Paper Money, Five Dollars Bill, 1776

Five Dollars ($5) South Carolina currency from 1776. Image of a horse surrounded by the inscription…

One Shilling (1 shilling) Vermont currency from 1781. Image of thirteen rings surrounded by the inscription - VERMONT CALLS FOR JUSTICE.

Paper Money, One Shilling Bill, 1781

One Shilling (1 shilling) Vermont currency from 1781. Image of thirteen rings surrounded by the inscription…

Four Dollars ($4) Virginia currency from 1776. Image is the new Coat of Arms for the State of Virginia.

Paper Money, Four Dollars Bill, 1776

Four Dollars ($4) Virginia currency from 1776. Image is the new Coat of Arms for the State of Virginia.

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. The circles meet in the center of the larger circle. The design is achieved by removing consecutive halves of the circles (semi-circles).

Circular Design

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal…

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal to the distance between the point of rotation and the center of the circle. The circles meet in the center of the larger circle. The design is achieved by removing consecutive halves of the circles (semi-circles).

Circular Design

Circular design made by rotating circles about a fixed point. The radii of the smaller circles is equal…

Formation of an image in the retina.

Image Formation in the Retina

Formation of an image in the retina.