Posted on 02/21/2024 7:21:04 PM PST by Red Badger
Decimals in a trigonometry table in Tabulae primi mobilis B by Bianchini, written in the 15th century. (Van Brummelen, Hist. Math., 2024)
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In 1593, German mathematician Christopher Clavius made a small mark that would change mathematics forever.
In a sine table in his treatise on the astrolabe, Astrolabium, he indicated the fractionation of a whole number by writing what has come to be regarded as the very first use of the decimal point.
There is, however, just one problem. According to new painstaking research by historian Glen Van Brummelen of Trinity Western University, this wasn't, in fact, its first instance. After poring painstakingly over historical documents, Van Brummelen found much earlier instances of the tiny notation.
In the 1440s, a young Italian merchant by the name of Giovanni Bianchini penned several astronomical works that made extensive and increasingly refined use of decimal points.
Van Brummelen convincingly argues Clavius merely copied the decimal point from Bianchini, who should be credited for his mathematical innovation.
A sine table in Clavius' Astrolabium, previously recognized as the earliest known use of the decimal point. (Van Brummelen, Hist. Math., 2024)
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Bianchini, born in around 1410, was a Venetian merchant who had probably been trained in arithmetic and algebra. Sometime in the 1430s, he was retained by the House of Este as an administrator of the estate; it was in this role that he penned his astronomical treatises, probably because his role involved astrological prediction for his noble employers.
He wrote five major works between 1440 and 1460: Tabulae astronomicae, on the motions of the planets; the Tabulae primi mobilis A, on spherical astronomy and mathematical astrology; the Flores Almagesti, his masterwork on mathematical astronomy; the Tabulae primi mobilis B, a rewritten version of the Tabulae primi mobilis A; and the Tabulae eclypsium, on the prediction of eclipses.
At that time in Europe, astronomy was performed using sexagesimal arithmetic; a system that uses 60 as its base the way our modern decimal system is based on units of 10. Though rarely used today, sexagesimal arithmetic has a lasting legacy in today's timekeeping.
Bianchini's Flores Almagesti starts with two chapters; the first on arithmetic, and the second on algebra. Giving such focus to these two topics might seem out of place in an astronomical work, but they set the groundwork for Bianchini's translation of mathematical astronomy from sexagesimal to a type of decimal arithmetic of his own devising.
Obviously Bianchini's system didn't really take; the sexagesimal system was still being used, much later, for astronomical calculations. But in his discussion of trigonometric functions in Tabulae primi mobilis B, Bianchini made his literal mark. Describing the use of interpolation to find the sine and cosine of an arc, he casually drops the number 10.4, and explains how to multiply it by 8, giving the answer 83.
The product of 10.4 and 8 is 83.2, but Bianchini's working shows that he is using the decimal point, and understanding it, the same way we use it and understand it.
A sine table in Tabulae primi mobilis B. (Van Brummelen, Hist. Math., 2024)
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Then, more dots show up in sine tables in the same work, in the interpolation column. This is exactly how the decimal point shows up in Clavius' Astrolabium, used in precisely the same way to perform the same function. And, tellingly, Clavius never uses it again, that we know of.
As someone who was a learned and respected scholar of astronomy, it's likely that Clavius knew of the work of Bianchini. This suggests an explanation for the decimal point's single appearance in Clavius' writings, Van Brummelen says.
"He had access to Bianchini's sine table (or to someone who himself had borrowed from Bianchini), and he copied the structure of that table in his own work," the historian explains in his paper.
"He recognized the usefulness of decimal fractional notation in the context of interpolation within a numerical table; but it was not his idea, and likely he had not invested significant effort himself to explore the use of the notation more fully. As a result, the origin of decimal fractional notation and the decimal point in Europe remained obscure until now."
It's such a mind-blowing discovery, and suggests that Bianchini's role in the complex and fascinating development of modern mathematics may have been somewhat overlooked. Perhaps there are more such discoveries out there, lurking in the pages of ancient books.
Van Brummelen's findings have been detailed extensively in the journal Historia Mathematica.
PinGGG!........................
Biden congratulated Bianchini personally and shook his hand while eating a can of Vienna sausage with him in Venice the day Biden helped Bianchini draw the first decimal point on the side of his lunchbox when they took a break building the indoor plumbing at the Taj Mahal in Prague for the first Olympics that Bart Starr won. It was the darndest thing he’d seen in his life.
I suppose both of those guys had a point.
🤦‍♂️...................................
A child was getting super stressed learning about decimals.
I guess you could say it was getting pretty tenths.
Just a fraction of their work.
It is likely someone else discovered earlier. Also, who is the first woman to use a decimal point? Handicapped person? Etc.?
I think it’s settled now period.
Well yes, but the crux of the biscuit is the apostrophe ......
I’m waiting on archaeologists for a carbon dating on decimal points in the petroglyph.
So we have a version 2.o?
In the 1990s, my employer rolled out a new internally-developed program that required entering values with decimals.
It was developed in Access in the US.
The program didn’t run in certain countries. After troubleshooting, they discovered that, say, in Finland, their domestic version of Windows recognized the COMMA as the decimal separator. This made the program incompatible.
The temporary work-around, was for the user to go to their Windows International settings and select UNITED STATES. The users was informed they’d have to “conform” to using the period as the decimal separator (and the comma as the thousand separator).
This may have screwed up local/domestic programs, but at least the US program worked.
It’s a “Point” . not a friggin coma , what’s with Europe anyway. What the @#$& is the reasoning behind this push to use a coma instead of a .
They use periods in phone numbers. Americans are starting to as well..............
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