Studied by 2 people
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
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)
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?
