Protractor (goniometer)

. . . . . . . . . . . . . . . . . Generic name for instruments used to divide circles and measure plane angles. They can be circular, semicircular or rectangular. To increase its accuracy, the protractor was often inserted in a nonius, a device for enhancing the precision of the measurements made by a direct readout on a graduated scale. The instrument often came with other accessories, such as folding metal arms and plumb lines. http://brunelleschi.imss.fi.it/museum/esim.asp?c=100176  

 

Main Entry: pro·trac·tor Pronunciation: \-ˈtrak-təәr\ Function: noun Date: circa 1611 1 a : one that protracts b : a muscle that extends a part 2 an instrument for laying own and measuring angles in drawing and plotting http://www.merriam-webster.com/dictionary/protractor

 

A protractor is any of a group of instruments used to construct and measure plane angles. The simplest protractor comprises a semicircular disk graduated in degrees—from 0° to 180°. It is an ancient device that was already in use during the 13th century. At that time, European instrument makers constructed an astronomical observing device called the torquetum that was equipped with a semicircular protractor. http://www.britannica.com/EBchecked/topic/480521/protractor  

The 360 degree circle is 4400 years old.

Origin of the 360-Degree Circle “Probable answer- A line of ancient peoples (Sumerians,

Akkadians, and Babylonians) who lived in Mesopotamia (now southern Iraq) invented writing, observed the skies, and invented a 360-degree circle to describe their findings. About 3000 BC, the Sumerians invented writing. They also had a calendar, dating from 2400 BC, that divided the year into 12 months of 30 days each, that is, 360 days. The Sumerians watched the Sun, Moon, and the five visible planets (Mercury, Venus, Mars, Jupiter, and Saturn), primarily for omens. They did not try to understand the motions physically. They did, however, notice the circular track of the Sun's annual path across the sky and knew that it took about 360 days to complete one year's circuit. Consequently, they divided the circular path into 360 degrees to track each day's passage of the Sun's whole journey. This probably happened about 2400 BC.

That's how we got a 360 degree circle. Around 1500 BC, Egyptians divided the day into 24 hours, though the hours varied with the seasons originally. Greek astronomers made the hours equal. About 300 to 100 BC, the Babylonians subdivided the hour into base-60 fractions: 60 minutes in an hour and 60 seconds in a minute. The base 60 of their number system lives on in our time and angle divisions.

A 100-degree circle makes sense for base 10 people like us. But the base-60 Babylonians came up with 360 degrees and we cling to their ways-4,400 years later.”

Origin of the 360-Degree Circle

According to Otto Neugebauer (in his The Exact Sciences in Antiquity), "A second Egyptian contribution to astronomy is the division of the day into 24 hours, though these hours were originally not of even length but were dependent upon the seasons." A little further on he says, "Thus our present division of the day into 24 hours of 60 minutes each is the result of a Hellenistic (Greek) modification of an Egyptian practice combined with Babylonian numerical procedures." The Babylonians/Mesopotamians used base 60 numbers in their business, astronomy, and mathematics (they used base 10 numbers as well). Probably connected to this was the division of the circumference of a circle into 360 parts by Babylonian astronomers. Geometric circles and the apparent movement of stars on the celestial sphere go naturally together and time is a common feature of astronomy. It was natural to use the division of a circle on a clock face. Neugebauer also says that, "The division of the circumference of the circle into 360 parts originated in Babylonian astronomy of the last centuries BC. The [base 60] number system as such is many centuries older and has nothing to do with astronomical concepts."

Why 360 degrees?

Probably because old calendars (such as the

Persian Calendar) used 360 days for a year -

when they watched the stars they saw them

revolve around the North Star one degree per

day.

Why has geometry not been 'metricked'? Why 360 degrees intstead of 1, 10, 100 or even 1000?

• It has been; there is the unit called the Grad of which 100 is a right angle (90 conventional degrees, or pi/2 radians). It originated in France as the 'grade' along with other metric units. The French artillery actually used it.

• The gradian or grad is the unit of measurement which is obtained by splitting a right angle (90 degrees) into 100 parts. The military have a fondness for this form of angle measurement and it is easy to obtain a compass set up this way.

• Angular measurement in degrees or radians is given in reference to a circle, 360 degrees or 2 Pi radians

•

• 2 pi radians = a full circle

•

1 radian = 57.2957 degrees

1 degree = 0.0174532 radians

Captain Joseph Huddart

1741-1816

Credited with inventing the 3 arm protractor in 1801

 

 

 

 

 

 

Source Definitions -

http://brunelleschi.imss.fi.it/museum/esim.asp?c=100176

http://www.britannica.com/EBchecked/topic/480521/protractor

http://www.merriam-webster.com/dictionary/protractor

http://www.google.com/#q=Why+is+a+circle+360+degrees%3F&hl=en&start=10&sa=N&fp=f11974faf5e3db50

http://www.wonderquest.com/circle.htm

Why 360 degrees.

Otto Neugebauer, The Exact Sciences in Antiquity

http://www.guardian.co.uk/notesandqueries/query/0,,-185569,00.html

http://www.mathsisfun.com/geometry/degrees.html

http://www.popsci.com/scitech/article/2002-02/who-determined-circle-should-be-divided-360-degrees

http://zonalandeducation.com/mmts/trigonometryRealms/radianDemo1/RadianDemo1.html

Calendars through the ages: Babylonian

U of Louisville: Babylonian magic and religion

U of Texas: Babylonian history, astronomy, math

Otto Neugebauer, The Exact Sciences in Antiquity

http://mathforum.org/library/drmath/view/59075.html

Huddart

http://www.barron.co.uk/Portrait+Reference+Library/Surnames+F+to+J/Huddart+Captain+Joseph+1741-1816

http://www.museumstuff.com/learn/topics/Joseph_Huddart

http://www.sosantikvarium.hu/metszo_terkepesz109.html

Google books

Use in the classroom – Protractors is new to 5th graders. This is a good intro to get their attention.

Further questions:

How do you use the protractor?

When is it best to use a circular protractor?

 

 

 

 

 

 

 

1. http://www.mathsinstruments.me.uk/page35.html  

 

Six inch rectangular ivory protractor by J Dunn of Edinburgh. Dunn was working from 1824 to 1841.  

 

An ivory, rectangular protractor by Robert Brettell Bate, Poultry, London. He was working from 1808 until he died in 1847. These protractors were frequently included in sets of drawing instruments.  

 

A nineteenth century, four and a half inch, boxwood protractor, probably from a pocket set.  

 

Six inch boxwood protractor from the James Parkes of Birmingham set of patent drawing instruments. Circa 1900.  

 

Two brass protractors. The upper, four inch, one is finely chamfered and hand engraved and would have come from a c1800 pocket case.  The lower, six inch, one is thin sheet brass, also hand engraved, probably c1900.  

 

This opaque, celluloid?, protractor dates from about 1920.  

 

An eight inch lacquered brass circular protractor dating from about 1900. This would probably originally have had its own mahogany case.  

 

A twelve inch, nickel silver plated brass, semi-circular protractor by Dobbie Son & Hutton of London. This heavy protractor also dates from about 1900. Protractors this large are rare.  

 

A Russian, nickel plated brass , seven inch protractor with extended scales and also diagonal scales on the base. It has a cloth covered and lined case. Probably mid-twentieth century.  

 

A heavy brass, six inch, vernier protractor by Troughton & Simms dating from the nineteenth century. It is housed in a fitted mahogany case and is complete with two screw-in points for holding it in position whilst plotting angles.  

 

Theo Alteneder eight inch, stainless steel, vernier protractor, mid twentieth century. It has a velvet lined case.  

 

Brown & Sharpe steel draftsman’s protractor, early twentieth century.  

 

A 1940s celluloid and japanned brass station pointer in its fitted wood case. The station pointer is a navigating instrument which can be used to plot ones position from angles measured between landmarks with a sextant. This one was possibly a training instrument. They are usually more heavily constructed, from brass or bronze.  

 

This protractor, by Harling, is from the Woolwich pattern military set and has elevation scales on the reverse. It is much wider than the normal type of six inch boxwood rectangular protractor.  

 

 

Hutchinson’s Stereographic Protractor for Circles 2.5 inches Radius. A celluloid rectangular protractor, 12” x 2.5”. Front has normal and stereographically projected angle scales top and bottom with instructions in the middle. Reverse has cm/mm and ¼ inch rulers and formulae. Arthur Hutchinson, FRS (1866-1937) was Emeritus Professor of Mineralogy at Cambridge University and Master of Pembroke College and invented (1908) and marketed

the protractor. This one has “117 Moorgate, London Maker” on it which was the address of W H Harling. The stereographic projection was used in a variety of disciplines including cartography, mineralogy, and crystallography.  

 

 

Folding arm vernier protractor by John Cail of Newcastle upon Tyne (working 1825-65). A six inch diameter brass protractor with inset silver scale and two silver verniers. The folding arms are supported by springs when extended and have protracting pins at their ends for accurate plotting. The protractor is adjusted by rotating a pinion which acts on a rack around the periphery of the instrument. These protractors were mainly sold for plotting theodolite readings. The protractor has a mahogany case and separate magnifier for reading the verniers.  

 

Heath & Co 6” circle station pointer, serial no. 5157, divided to ½ degree, with flush verniers reading to 1 minute and tangent screws for fine adjustment. 15” arms with extensions to 24”. Separate magnifier for reading the verniers. Wooden box with mahogany sides and plywood top and bottom, fitted and part lined with green felt. This is similar to the Admiralty Pattern station pointer shown in the 1958 W F Stanley catalogue except that it does not appear to be divided on brass or chrome plated. Heath & Co merged with Stanley in 1926, but the name was retained for navigational instruments.  

 

Nickel silver station pointer by Bottomley, 11 Billiter St., London, dating from 1878-88 when Bottomley was at that address. The bottom arm, which is signed, is missing its index. The magnifier is missing from its housing in the case. Four inch circle.  

 

Brass protractor by Robson, Newcastle upon Tyne, probably ca.1880. In addition to being graduated in degrees it has the four cardinal points marked on it, suggesting that it was for navigational use. Diameter 7.4 inches.  

 

 

Lechertier Barbe ivory, six inch, rectangular protractor, ca.1900. This is a typical protractor of the period.  

 

 

Two six inch rectangular protractors. The upper one, in ivory, is by Negretti & Zambra and dates from c1900. The lower, brass one is a British Army “A II Protractor 6” x 2” Exactly” dating from 1917 made by the Tone Engineering Co Ltd, Birmingham.  

 

 

Ivory protractor by Aston & Mander with military sketch-mapping scales on the reverse including “Yds 8 ins to 1 mile”; “Normal scale of slopes” and a table of “HE in Yds” columns “D, 15’, 20’” with the formula “HE = VI x 19.1/D”, where HE = Horizontal

Equivalent, VI = Vertical Interval and D = Degree. 15’ & 20’ are contour intervals (VI) in feet.  

 

 

Hughes Label Co Ltd 81562 AII Protractor 6” x 2” Exactly. Marked with the broad arrow, this was the standard British army map reading protractor in the First World War. This one is celluloid but I also have examples in boxwood and in brass (Tone Engineering - see above)  

 

 

Aston & Mander 1917 Ltd. rectangular protractor, made of ivory, intended for use with English and continental maps, probably for use by an army officer. Aston & Mander made many items for the army and later for the RAF including various designs of rectangular protractor. This version is quite similar to the 'Protractor Rectangular 6" x 2" Exactly AII' (see above), which was made for the army by several makers in a variety of materials including brass, boxwood and white celluloid. This Aston & Mander protractor, being ivory, would not have been army issue but probably purchased by the officer himself as officers had to purchase much of their own equipment.