SH Archive How did Ancient Romans calculate complex numbers?

[KD Archive]

Ancient Romans are credited with construction of quite a few of remarkable buildings (we know it's questionble). Here is an example of some of those: Top 10 Magnificent Ancient Roman Architectures.

Amphitheatre Nimes

Sure mathematical calculations were required to engineer buildings of such complexity, yet Roman Numerals are anything but user friendly. The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700. A distinctive West Arabic variant of the symbols begins to emerge around the 10th century.

And I'm not even talking about decimals, fractions, or anything of that nature. Here is an example of some "simple" calculations using Roman Numerals.

• 746+124=870 [=] DCCXLVI+CXXIV=DCCCLXX
• 46×12=552 [=] XLVI×XII=DLII
• 78+36x42=1590 [=] LXXVIII+XXXVI×XLII=MDXC

* * * * *
​

We use calculators for adding a few currency units here and there. What did Ancient Romans use to calculate complex numbers? Even simple ones are beyond hard. Of course we can say that they had plenty of practice... but really?

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[Archive]

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Username: humanoidlord
Date: 2018-05-14 23:39:51
Reaction Score: 5

Ancient Romans are credited with construction of quite a few of remarkable buildings (we know it's questionble). Here is an example of some of those: Top 10 Magnificent Ancient Roman Architectures.

Amphitheatre Nimes
View attachment 2870

Sure mathematical calculations were required to engineer buildings of such complexity, yet Roman Numerals are anything but user friendly. The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700. A distinctive West Arabic variant of the symbols begins to emerge around the 10th century.

And I'm not even talking about decimals, fractions, or anything of that nature. Here is an example of some "simple" calculations using Roman Numerals.

• 746+124=870 * -------- * DCCXLVI+CXXIV=DCCCLXX
• 46×12=552 * ----------- * XLVI×XII=DLII
• 78+36x42=1590 * ------ * LXXVIII+XXXVI×XLII=MDXC

* * * * *

We use calculators for adding a few currency units here and there. What did Ancient Romans use to calculate complex numbers? Even simple ones are beyond hard. Of course we can say that they had plenty of practice... but really?

this why i love this website! it makes me question things that i otherwise take for granted!
i know by past experience that even writing numbers in roman is kinda hard, i cant even imagine how hard calculations were!

 

[Archive]

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Username: CyborgNinja
Date: 2018-05-15 02:24:03
Reaction Score: 2

The system we use is quite reliable and the only comparable system from the ancient world is the Persian system which you mentioned. Our numbers are just a derivative of their numbers. Could it be that they just used exactly what we use. How modern is our number system anyway. If it's being used in Gothic texts it must be from the tartar era. Isn't our font known as roman?

There aren't any extremely old examples of out number system to point to but that doesn't mean it wasn't what they used back then. Maybe the Arabic numerals was the generic globally used system and we've obly recently split from it.

 

[KD Archive]

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Username: KorbenDallas
Date: 2018-05-16 01:55:11
Reaction Score: 1

Pretty sure they did not mess with this "DCCXLVI+CXXIV=DCCCLXX". Yet, wondering how the official historians explain their (Ancient Romans) calculation methods.

 

[Archive]

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Username: tupperaware
Date: 2018-12-18 03:55:45
Reaction Score: 1

Phew, I thought you meant these complex numbers.

and that somebody pulled out of the secret Vatican library another copy of a copy of something that Diophantus allegedly wrote. Some interesting StackExchange - Why there are there no known Roman mathematicans from the Roman Empire?

 

[Archive]

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Username: ISeenItFirst
Date: 2018-12-18 07:53:30
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Maybe they called the numbers by Roman numerals but used an abacus or something similar for calculations. Just a thought.

 

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Username: CyborgNinja
Date: 2018-12-18 09:01:55
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StackExchange - Why there are there no known Roman mathematicans from the Roman Emp

Here's the top votes answer from that link:

Roman empire did not consist of Latin-speaking "Romans" only. It included Greece, North Africa and what we call now Middle East. Probably a majority of the inhabitants of the Roman empire were Greek-speaking. And there were mathematicians among them. Menelaus, Ptolemy and Diophantus were living in the Roman empire. Some of them could be Roman citizens, some not. We know practically nothing about their lives. Most likely all were Roman citizens after the citizenship was granted to all residents of the empire.

So the correct questions would be:

Why Roman mathematicians wrote in Greek?

Why most of them preferred Africa for their residence?

And the answer is that there was a tradition among the Greeks, in Greek language, especially in the Middle East, especially in Alexandria. Tradition means schools, libraries, scientific environment. This environment was created by the Greeks in the Hellenistic times, and partially survived almost to the end of the Roman empire.

By the way, many Roman works in applied sciences and engineering were also written in Greek. See a related discussion here:

Roman engineers

Greek was the language of science in the Roman empire. Like Latin was the language of Science in Europe in 16-18 centuries.

So everyone in europe spoke greek which is the same alphabet as Latin which is the same as Cyrillic. Nothing here weakens the stolen history hypothesis.

 

[KD Archive]

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Username: KorbenDallas
Date: 2020-01-24 06:03:31
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Love this image here.

 

[Archive]

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Username: tupperaware
Date: 2020-01-24 06:31:36
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Love this image here.

View attachment 39224

Below is a multiplication table for roman numerals. The applied math users of the day would have at least this memorized as well as addition, subtraction and division tables. Past that there could have been mental math tricks. Here are the basics. Roman Numerals (Totally Epic Guide.) - Know the Romans They also probably had something like an abacus for division and the rest.

 

[KD Archive]

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Username: KorbenDallas
Date: 2020-01-24 06:41:43
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This is just insane: 1-1000

LXXIV * XII = DCCCLXXXVIII aka 74 * 12 = 888

 

[Archive]

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Username: tupperaware
Date: 2020-01-24 07:18:32
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This is just insane: 1-1000

LXXIV * XII = DCCCLXXXVIII aka 74 * 12 = 888

Lots of insane cultures back then. The Roman math wizzes probably made good money.

 

[BStankman]

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Username: BStankman
Date: 2020-01-24 10:17:59
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Below is a multiplication table for roman numerals. The applied math users of the day would have at least this memorized as well as addition, subtraction and division tables.

I think you are on to something here. Prior to the electronic calculator, memorization of tables was key to success in math.

It seems insane to us, because we have devolved so far in 400 or 500 years, but the average "Roman" carpenter or mason probably had these memorized at a very young age.

Here is a math test a 13 year old would have taken 100 years ago in frontier Kansas.
Extrapolate that back another 3 or 4 times to get a sense of the devolution.

Arithmetic (Time, 1.25 hours)
1. Name and define the Fundamental Rules of Arithmetic.
2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold?
3. If a load of wheat weighs 3942 lbs., what is it worth at 50cts. Per bu., deducting 1050 lbs. for tare?
4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven
months at $50 per month, and have $104 for incidentals?
5. Find cost of 6720 lbs. coal at $6.00 per ton.
6. Find the interest of $512.60 for 8 months and 18 days at 7 percent.
7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $20 per >>m?
8. Find bank discount on $300 for 90 days (no grace) at 10 percent.
9. What is the cost of a square farm at $15 per acre, the distance around
which is 640 rods?
10. Write a Bank Check, a Promissory Note, and a Receipt.