CPSC 409 Midterm 1

Chinese, Japanese

The abacus origins are unclear but it is used by many cultures, e.g ____________ and ____________

Semitic

The origin of the word abacus may come from the _______ word abaq, meaning “dust”

1200

The abacus has also influenced the English language

* Historically \~(_____AD), “arithmetic” and “abacus” became interchangeable
* Romans: The pebbles were called “calculi” from which “calculate” and “calculus” were derived

Astrolabe

A 2 and sometimes 3 dimensional representation of the celestial sphere

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Used for many purposes:

* Mapping the position of celestial bodies
* Measuring latitude/determining approx location
* Determining time
* Estimating the height of objects
* Casting of horoscopes

Edmund Gunter

Gunter’s Quadrant was invented by ____________

1581, 1626

Edmund Gunter lived from _____ to _____

astrolabe

Gunter’s quadrant was based on the ________

* Basically folded it into a quarter circle
* Used to solve the same sort of problems

Proportional Compass

Used by draftsmen to reduce and enlarge drawings in any given proportion

1584, 1606

Independently there were many publications that described THE SECTOR that occurred from _____ to _____

1606, Padua, Galileo

The most widely copied version of THE SECTOR was created in ______ in __________ by __________

Geometric and Military Compass

Initially used to solve artillery calculations all of which affected the range

* Galileo Galilei

Gelosia

Has probably origins in India, and later Arab, Persian, and chinese societies by the middle ages

1550, Scotland, logarithms

John Napier was born in _____ in _____

* Best known for the invention of __________
* Napier’s bones

Napier’s Bones

Used to perform multiplications and calculate logarithms

* A collection of all possible columns in the Gelosia table

Henri Genaille

Worked as a civil engineer for a railway

Edouard Lucas

A french mathematician

* (invented a certain ruler)

Genaille-Lucas Rulers

* Similar to the Napier bones but didn’t require the operator to remember the carry

Differential Analyzer

Helps with determining the area under a curve. Solving differential equations

* Early attempts to devise mechanisms for solving these problems were hindered by the limited ability to obtain accurately machined parts

Vannevar Bush, MIT, 1920, 1931

First to produce a working Differential Analyzer was ______________ from the school _____ in the late _____s. Publication occurred in _____

mechanical movement

Programming and debugging the differential analyzer was difficult because it relied heavily on _________________

Manchester, MIT, Oslo

At least 5 copies of the differential analyzer were made at the schools: _____ _____ and _____

WWII Norway

Differential Analyzers had a military application through artillery and rocket trajectories. It was utilized in ____ _______

* Shortly after the successful German invasion
* Oslo University
* MIT

Set up, selector, registering mechanism, carry mechanism, control mechanism, erasing mechanism

The 6 basic elements of almost all mechanical calculators

set up

Components of mechanical calculators:

Allows the number to be entered

Selector

Components of mechanical calculators:

Determines the type of operation

Registering mechanism

Components of mechanical calculators:

Indicates the value of a stored number (result)

carry mechanism

Components of mechanical calculators:

Determines that any carries are handled properly

Control mechanism

Components of mechanical calculators:

Ensures that the gears are properly aligned at the end of each operation (avoid false results and jamming)

Erasing mechanism

Components of mechanical calculators:

Reset the result register between operations

Wilhelm Schickard

Developed the first true adding machine which could handle a carry (debatable, maybe attributed to Bruno von Freytag Loringoff)

* Professor of Hebrew, oriental languages, math, astronomy, geography
* Hobbies: painting, mechanic, engraver

Evidence of the machine:

* A letter sent to/from Johannes Kepler (mechanical equivilant of his manual calculations)

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1592, 1635

Wilhelm Schickard lived from ___ to ___

fire, plague

What happened to Shickard’s calculators?

* One perished in a _____
* The second is believed to have been disposed of after Schickard’s family died in a _____

Pascal’s wager

1623, 1662

Blaise Pascal lived from ______ to ______

Blaise Pascal

* Born in Southern (Clermont) France
* Lots of his life is greatly exaggerated
* Credited as the next major attempt to produce a calculating machine
* Home schooled in the basics of reading and writing by his father Etienne Pascal
* His family were government tax collectors that did very repetitive and tedious calculations

1642

Pascal designed his first calculating machine at the age of 19 in _____

* But had trouble trying to find someone to implement the design

1662

Pascal suffered from a painful illness which led to his death at 39 in ______

1646, 1716

Gottfried Leibniz lived from ______ to ______

Gottfried Leibniz

* Accepted into unversity of Leipzig for law at age 15
* Applied for his doctorate of law at age 20
* Doctorate awarded at the university of Altdorf

Oliver

To create Leibniz’s final machine, he enlisted the aid of M. ______

Leibniz’s Calculating Machine

* Used a gear based system (not single tooth gear) for carries
* Carries were problematic
* Ripple carry through several digits had to be manually propogated

Schickard, Pascal, Leibniz

Whose machines offered the addition opperation?

Pascal, Leibniz

Whose machines offered the addition and subtraction operation?

Leibniz

Whose machines offered the addition and subtraction operation?