Calculus was invented in the late 1600s, almost 2000 years after the Roman aqueducts were built. The Roman engineer would know some geometry, but certainly not calculus.
The mathematics mentioned in the first source have nothing to do with engineering though.
Ratios, a little trigonometry and geometry, all of which are essentially under the geometry category and arithmetic are not what concerns the engineering field. They are architectural tools if you will. Of course they utilized geometry, that’s not something innovative. Maths in general does not mean anything here, maths can be about number theory(completely unrelated to any practical application).
What differentiates them and engineers now is essentially mechanics. Forces, torques, stresses, materials, masses, moments of inertias etc. They never applied quantitative engineering principles, their structures were only sound from experience and intuition, the geometry mentioned was for architectural purposes.
Astrology was so important to the Greeks, they figured out the elliptical orbits of the planets (up to Jupiter) and how to compute them without calculus.
Romans had a basic understanding of proportions and general vibes of design, but they couldn’t really create calculations to verify their design as we do today. For instance, the designers of the Pantheon understood they needed to lighten the concrete as it went up and had novel techniques of doing so that we use today, but they didn’t really know.
The state of the art for understanding basic stresses didn’t become known until the 19th century. The design of the Eiffel Tower was impressive, in part, because that structure has a calc book defending it. A lot of early railroad bridges were still designed based on ratios and vibes.
That said, not all loads were understood by that time. The Tacoma-Narrows Bridge collapsed in part because of a gross misunderstanding of wind loads combined with the ability to design structures light enough that wind loads controlled.
Calculus is a specific field of mathematics, mostly to do with limits, integrals and derivatives. Those all feature very heavily in working out loads and stresses.
But it’s unfair to say the Roman didn’t have calculus. It wasn’t formal calculus, but they absolutely had mathematics, and the Greeks worked out the exhaustion method a century before the Via Appia was even started.
You don’t need calculus to do some very impressive building, you can go very very far with experience, rules of thumb and basic maths. Hell, ask any civil engineer and they’ll gladly show you some common formula that makes physicists cry.
Put simply, you don’t need to know of, or what a certain field of math is to be able to apply the different fundamentals of it.
As an example.
You ever see a basketball player bring out a chalkboard to calculate the trajectory, mass, spin, or force to throw the ball to get it in the basket? No. Over time they all eventually create a physics model in their heads and are able to subconsciously calculate all of that with relative accuracy based on experience, training, and practice. Yet, a lot of those players never took a lick of physics.
Tbh, I want my memes with sources. and this one is strange…
https://civilizationchronicles.com/roman-engineering-and-mathematics/ claims that mathmatics were essensial to roman engineering.
whereas this (only abstract avaliable…) https://link.springer.com/chapter/10.1007/978-3-662-66494-0_25 claim that mathmatics were but an auxillary science? 🤔
nontheless mathmatics seems to have been quite understood and used by the roman engineers building among other things, aqueducts
Calculus was invented in the late 1600s, almost 2000 years after the Roman aqueducts were built. The Roman engineer would know some geometry, but certainly not calculus.
The mathematics mentioned in the first source have nothing to do with engineering though.
Ratios, a little trigonometry and geometry, all of which are essentially under the geometry category and arithmetic are not what concerns the engineering field. They are architectural tools if you will. Of course they utilized geometry, that’s not something innovative. Maths in general does not mean anything here, maths can be about number theory(completely unrelated to any practical application).
What differentiates them and engineers now is essentially mechanics. Forces, torques, stresses, materials, masses, moments of inertias etc. They never applied quantitative engineering principles, their structures were only sound from experience and intuition, the geometry mentioned was for architectural purposes.
The joke is that calculus as a field of mathematics didn’t exist until millennia after the fall of the empire
Astrology was so important to the Greeks, they figured out the elliptical orbits of the planets (up to Jupiter) and how to compute them without calculus.
Right, I’m not denying that. People have always been smart. The problem that calculus solved was the intensely difficult algebra that it replaced
ironically, algebraists are currently trying to replace calculus with more algebra. needless to say, the algebra involved is pretty extreme
Romans had a basic understanding of proportions and general vibes of design, but they couldn’t really create calculations to verify their design as we do today. For instance, the designers of the Pantheon understood they needed to lighten the concrete as it went up and had novel techniques of doing so that we use today, but they didn’t really know.
The state of the art for understanding basic stresses didn’t become known until the 19th century. The design of the Eiffel Tower was impressive, in part, because that structure has a calc book defending it. A lot of early railroad bridges were still designed based on ratios and vibes.
That said, not all loads were understood by that time. The Tacoma-Narrows Bridge collapsed in part because of a gross misunderstanding of wind loads combined with the ability to design structures light enough that wind loads controlled.
The engineer guy on YouTube did an episode the engineering method explaining how ancient and medieval Masons built stuff without math. https://youtu.be/_ivqWN4L3zU?si=2N_iyZiBD8eDpltR
Though I am sure the Romans used plenty of math during the construction of many of their projects.
Calculus is a specific field of mathematics, mostly to do with limits, integrals and derivatives. Those all feature very heavily in working out loads and stresses.
But it’s unfair to say the Roman didn’t have calculus. It wasn’t formal calculus, but they absolutely had mathematics, and the Greeks worked out the exhaustion method a century before the Via Appia was even started.
You don’t need calculus to do some very impressive building, you can go very very far with experience, rules of thumb and basic maths. Hell, ask any civil engineer and they’ll gladly show you some common formula that makes physicists cry.
Put simply, you don’t need to know of, or what a certain field of math is to be able to apply the different fundamentals of it.
As an example. You ever see a basketball player bring out a chalkboard to calculate the trajectory, mass, spin, or force to throw the ball to get it in the basket? No. Over time they all eventually create a physics model in their heads and are able to subconsciously calculate all of that with relative accuracy based on experience, training, and practice. Yet, a lot of those players never took a lick of physics.
Do you happen to know any civil engineers, I would like to see these formulas
when we approximate g to 10 they weep.
π=3