Early Computational Devices

Question 1

What is the first approach described for finger counting?

Answer 1

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Question 2

What is the binary notation for finger counting?

Answer 2

ah

Question 3

What is the Chinese notation for finger counting?

Answer 3

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Question 4

How do you represent number on the Chinese Abacus?

Answer 4

adg

Question 5

How do you represent numbers on the Japanese Abacus?

Answer 5

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Question 6

What was the influence of the Abacus on language?

Answer 6

– Historically ~1200 AD ‘Arithmetic’ and ‘abacus’ became interchangeable
– Romans: the pebbles used were called ‘calculi’ from which ‘calculate’ and ‘calculus’ were derived.

Question 7

How can you represent different values with the table abacus?

Answer 7

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.

Question 8

What are some common uses of the astrolabe?

Answer 8

– Mapping the position of celestial bodies
– Measure latitude / Determining approximate location – Determine time
– Estimate the height of objects
– Casting of horoscopes.

Question 9

What are the origins and approximate time period of the invention of the astrolabe?

Answer 9

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Question 10

What are some common uses of the quadrant?

Answer 10

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

Question 11

What is the approximate time period of the quadrant?

Answer 11

ag

Question 12

How was a proportional compass used?

Answer 12

to reduce and enlarge drawings in any given proportion (like a protractor)

Question 13

Who was widely attributed as the creator of the sector?

Answer 13

Galileo

Question 14

How was a sector used for artillery calculations?

Answer 14

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Question 15

How can one preform multiplication using the Gelosia Method?

Answer 15

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

Question 16

How were Napier’s Bones used for calculations?

Answer 16

• 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

Question 17

How does one do multiplication using Genaille–Lucas rulers

Answer 17

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

Question 18

How does one do division using Genaille–Lucas rulers

Answer 18

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Question 19

Who created logarithms?

Answer 19

John Napier

Question 20

How can logarithms be used to solve complex equations?

Answer 20

By putting the geometric and arithmetic sequences side by side people could quickly make calculations that would’ve been difficult to compute back then.

Question 21

Which mathematical functions can be computed with a slide rule?

Answer 21

multiplication, division, trigonometric calculations, roots and powers

Question 22

Who is credited with inventing the modern slide rule?

Answer 22

Amedee Mannheim

Question 23

What are some difference between the older and modern slide rule?

Answer 23

Modern slide rule incorporates transparent cursor

Question 24

How does the modern slide rule compute multiplication?

Answer 24

Mechanical implementation of logarithm tables