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Leonardo Da Vinci And Algebra


belovelife

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Through the libraries I rambled

I read lots of funny books...

 

An interesting read was "Pi in the sky"

by Matematician John D.Barrow.

 

He traces the movements of early man by the number

system they use...Approximation:

 

1 one two many

2 one two (ahem i seem to have forgotten the details!)

x Up to the decimal system

Z No calculus im afraid :)

 

The places most far from Africa (and in south africa)

has tribes still using the first system,

so where/when and how are the origins of improvements?

 

Keep on searching :)

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i remember reading about da vinci once, and it explained that at the time in europe, algebra was not tought, and he once got scolded for bringing it up in class,

This would surprise me, BL. It’d be useful for you to give a reference to where you read this, as I’m fairly certain it’s from one of many fictional treatments of the childhood of Leonardo.

 

Little is actually known about Leonardo’s childhood, because little about it by him or others was either ever written, or if written, has survived and been discovered. Because he could write (in Latin), and do fairly advanced (for his time – he wouldn’t be considered arithmatically competent by present day high-school standards) numeric calculations, and because we know he was (as wasn’t unusual for an illegitimate child of a minor nobleman in the 1450s in a small town like Vinci) fairly well provided for as a child, it’s reasonable to assume he learned Latin and math as a child, from a private tutor, but the name and identity of that tutor is unknown. Not until he was apprenticed to a well-know visual artist (Andrea di Cione, known professionally as Verrocchio) in nearby Florence, at the age of 14-15, do we begin to have much record of Leonardo. It’s likely that this was when he had a non-hassle supply of paper, and was encouraged to use it to practice drawing, that he began keeping a sort of diary, which would eventually be known to us as Leonardo’s Notebooks, consist of about 4,000 surviving pages of rag-based (better and longer-lasting than our common wood pulp based) paper.

 

These pages survived only because, after Leonardo was a successful artist with his own apprentices, he willed all of his works to a favorite former apprentice, Francesco Melzi, who kept them safely locked up from Leonardo’s death in 1519 until his in 1570. Melzi’s heirs, unfortunately, sold some of the papers (Leonardo being a famous name, they were worth a lot, to the right buyer), resulting in some, but fortunately not all, of them being lost.

 

We had another stroke of luck in 1630, when successful and famous sculptor Pompeo Leoni (who had an interesting life, being what we’d these days call an ex-con you don’t wanna mess with!) got hold of most of the notebooks, and organized them thematically into several volumes (unfortunately, losing most of the information about the order in which they were originally written and assembled by Leonardo), where they remained mostly intact, finding their ways into various museums and private collections. There are 10 of these volumes, known as codices (singular: codex).

 

By around 1800, knowledge of the existence of the notebooks, and thus that Leonardo was anything but a brilliant painter, mediocre sculptor, and poor workforce manager, was only somewhat known. Some historians write of him as a great painter, others, having seen one or more of the codices, describe his as a “universal genius”. Some, to this day, conclude he was an engineer and inventor, though there’s scant evidence many of his designs were ever prototyped or successfully built, and lots of modern proof that most of them, like his famous “helicopter”, simply couldn’t work.

 

In short, it’s a wise to keep in mind that most of what we “know” about Leonardo was made up long after his death. Because of his self-portraits, we know what he looked like. Because of his paintings, sculptures, and notebooks, we know how he drew, painted, and sculpted, and that he was interested in science and technology. The rest is guesswork and fiction.

 

(sources: http://www.unmuseum.org/leosketch.htm, wikipedia links above, http:// http://www.hypatiamaze.org/leonardo/leo_lune.html, link from BL’s post, http://www.hypatiamaze.org/leonardo/leo_timlin.html)

 

but at the time the mayans and aztec had calculus?

Be careful here!

 

The work “calculus” is used sometimes to mean “a method of counting”, but most commonly refers to the mathematics of (I necessarily oversimplify to summarize here) finding exact representations of infinite sums of infinitesimal numbers, what we these days call “Newton’s and Leibniz’s Calculus”, though its early concepts were developed by people who lived before Newton or Leibniz were born, and has been significantly expanded and revised ever since.

 

Mayans had various documented techniques for counting and doing fairly simple arithmetic – addition and subtraction only. It involved using various fairly standard tables, much as students do in elementary school today, which were reproduced and distributed to trained scribe/”calculationists”. Much of their cleverness was due to the fact that they used some really awkward numeral schemes, mostly base 20, but sometimes with different bases, such as 18, thrown in a particular position.

 

There’s some evidence that “high level” Mayan scribes could, with difficulty and to some extent, multiply and divide large numbers, but they appear to have used cleverness and tricks, not techniques that could be done quickly and for all numbers, or taught to every scribe.

 

They certainly couldn’t do the sort of math Cavalieri, Newton, and Leibnitz did.

 

(Sources: wikipedia article calculus; any of various articles on “Mayan arithmatic”, such as http://www.gap-system.org/~history/HistTopics/Mayan_mathematics.html)

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i can't remember the name of the book, it was a biography of leonardo, at the beginning of the book, it stated that at the time, moors were getting popular for their status in education, a shipment of book was just recieved from china replacing the books burned in the book burnings of europe, of which were translated originally at the great library of alexandria

 

and it descibed a scene where he introduced the basic idea of a vaaryable to his teacher, and he got scolded,

 

so he went to the hills and drew birds instead

later on he was made an apprentace

 

furthermore, the pobotic show he made for a wedding, stuff, was also robotics in nature,

 

which can relate to the japanese tea ceremony

 

 

 

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now on the topic of calculus, this is an interresting debate, because of all the lies that were fed to immigrants from europe, to encourage conquering the people,

 

the mind"s eye of the people got demonised, so most of the history you read and learn is completely false

 

the thing is, dispelling this view is difficult , considering it is still tought in schools

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