Early Computational Devices Flashcards
What is the first approach described for finger counting?
add
What is the binary notation for finger counting?
ah
What is the Chinese notation for finger counting?
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How do you represent number on the Chinese Abacus?
adg
How do you represent numbers on the Japanese Abacus?
add
What was the influence of the Abacus on language?
– Historically ~1200 AD ‘Arithmetic’ and ‘abacus’ became interchangeable
– Romans: the pebbles used were called ‘calculi’ from which ‘calculate’ and ‘calculus’ were derived.
How can you represent different values with the table abacus?
lines act as ones, spaces acts as 5, the number of circles on the spaces and lines is the quantity of that value. So the overall number being represented is the sum of the values represented by the circles.
What are some common uses of the astrolabe?
– Mapping the position of celestial bodies
– Measure latitude / Determining approximate location – Determine time
– Estimate the height of objects
– Casting of horoscopes.
What are the origins and approximate time period of the invention of the astrolabe?
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What are some common uses of the quadrant?
It was used to find the hour of the day, the sun’s azimuth, and other common
problems of the sphere or globe, as well as to take the altitude of an object in degrees
What is the approximate time period of the quadrant?
ag
How was a proportional compass used?
to reduce and enlarge drawings in any given proportion (like a protractor)
Who was widely attributed as the creator of the sector?
Galileo
How was a sector used for artillery calculations?
sdf
How can one preform multiplication using the Gelosia Method?
So you start bottom-right
And add the boxed elements of each diagonal, making sure to process any carries which might exist forwards as you traverse upwards
So, ignoring the cell errors in this case, we start with the bottom right cell-part (8)
to get the first diagonal
then add (0-4-2) to get the 6
then add (2-4-0-1-6) to get 13, giving us 3 in the third-from-right diagonal and a carry of 1 into the next summation
thus, the fourth-from-right diagonal is then summing (3-8-1-5-0-1), giving us 18 (an entry of 8 and a carry of 1)
likewise, the second-last diagonal is then summing (0-4-1)
and the last diagonal remains zero because there is no carry
How were Napier’s Bones used for calculations?
- one number on top
- one number on the left
using the row of the number on the left, go through the whole row where the leftmost half diamond is the most significant digit and rightmost half diamond is the least signficant digit. the sum of each full diamond between these 2 is the remaining digits
https://www.youtube.com/watch?v=1nWT-zbb3s8
How does one do multiplication using Genaille–Lucas rulers
Take larger operand and create it with rulers, then get a index ruler on the left side. Then you go to the ruler representing the ones digit and count down groups until you reach the second operands group number. Then read the first value in the group and follow it’s arrow to the next value in the next ruler and keep doing that until you have read from all rulers.
https://youtu.be/8CoNctAjQY0?list=PLTma1no4UaZvK12abFsZBOYX0gWgVyNU4
How does one do division using Genaille–Lucas rulers
sdf
Who created logarithms?
John Napier
How can logarithms be used to solve complex equations?
By putting the geometric and arithmetic sequences side by side people could quickly make calculations that would’ve been difficult to compute back then.
Which mathematical functions can be computed with a slide rule?
multiplication, division, trigonometric calculations, roots and powers
Who is credited with inventing the modern slide rule?
Amedee Mannheim
What are some difference between the older and modern slide rule?
Modern slide rule incorporates transparent cursor
How does the modern slide rule compute multiplication?
Mechanical implementation of logarithm tables
