One of the current book bundles at HumbleBundle contains 3 books by John Horvath and Rich Cameron featuring #OpenSCAD for visualization and examples (among 15 in total with various topics on electronics and robots).
Who do we have to blame for cos⁻¹𝑥 meaning the inverse function (arc cosine), but cos²𝑥 meaning the square of the cosine?
Today I did a little reading in Florian Cajori's "A History of Mathematical Notations" and found that it's none other than William Herschel (discoverer of Uranus.) He acknowledged that that the superscript notation already meant exponentiation, and thus that cos⁻¹𝑥 already meant something different, but insisted that the right thing was to use superscripts for iteration and inverses. After all, we already used 𝑑², 𝑑³, etc. for iterated differentiation (so if you want to blame Liebniz instead, I guess that's fair.)
And so we got stuck halfway, because inverse sine is useful, and sine to a power is useful, but iterated sine not so much.
Started our trigonometry unit yesterday and shared one of my favorite articles from Evelyn Lamb: Ten Secret Trig Functions Your Math Teachers Never Taught You.
I'm thinking about putting a haversine identity on the next test.
I’ve been working with the LEEDS 2023 Year of Culture on telling their story with data. You can look at the data microsite that I built along with the team at Open Innovations here -> https://data.leeds2023.co.uk.
I’ve had fun on the last proper day before Christmas making a page which lays out the striking ward motifs created during The Gift project in the same layout as our hex maps. I think it looks lovely!
3,700-year-old Babylonian stone tablet gets translated, changes history
They were doing trigonometry 1500 years before the Greeks.
Most historians have credited the Greeks with creating the study of triangles' sides and angles, but this tablet presents indisputable evidence that the Babylonians were using the technique 1,500 years before the Greeks ever were.
Mansfield and his team are, understandably, incredibly proud. What they discovered is that the tablet is actually an ancient trigonometry table.
STOP DOING #MATH#anime
• TRIANGLES were not supposed to be given #animation
• YEARS of #trigonometry yet NO REAL-WORLD USE FOUND for going sharper than a CIRCLE
• Wanted to remove all edginess for a laugh? We had a tool for that: it was called #moe
• "Yes please give me A Cruel Angle's Thesis. Please give me an OP version of it"—Statements dreamed up by the utterly Deranged
> I feel like I'm the only person on the Internet who took geometry in high school.
That's 'cos while lots of us took it, we don't hang out together much. (cough)
Oddly, geometry & trigonometry is one of the things I learned in high school that I still use to this day. It comes up in all kinds of software engineering that has no obvious connection to graphs, plots, GIS, or anything like that.
For all the students out there: I used #trigonometry and queue #DataStructures to solve two different real world problems at work today. Don’t forget the basics!
@ColinTheMathmo students in US generally encounter sine & cosine in geometry class during 9th or 10th grade. They are introduced as ratios of sides in right triangles (along with tangent).
No graphing of trig functions or unit circle til much later, usually PreCalculus (2 years later).
Some schools introduce unit circle and radian measure earlier than Precalc, the smoothest way to create unit circle IMO is to build it from special right triangles (30-60-90 & 45-45-90). Radian measure is usually really confusing to Ss , they often memorize the conversion "180° = pi radians" without really grasping what it's all about.
⚠️ 1 element, no pseudos
⚠️ no SVG, no images in general save for CSS gradients
🚫 no JS
⚠️ no lists of values of length > 8
⚠️ same amount of compiled CSS regardless of whether we have 6 or 25 bars
⚠️ at most 7 CSS declarations
An interesting and original (I think) puzzle from Micky Bullock.
"Last week Negligent Neil calculated length AC. He had forgotten to switch his calculator from radians to degrees but, fortunately, he still got the answer right.
"An inky splodge has now obscured the angle at A. Negligent Neil has forgotten what his answer was for length AC, but he insists it was between 40 cm and 50 cm.
Also known as the father of #algebra,
Al-Khwarizmi's #book, "Compendious Book on Calculation by Completion and Balancing” introduced systematic methods for solving linear & quadratic equations.
Using letters as symbols to represent unknown quantities, lay the foundation for symbolic algebra.