haversine is incredibly useful when you're doing quick distance calculations between points on the Earth though...
Obsolete trig functions and why we don't use them anymore (2013)
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Re: Obsolete trig functions and why we don't use them anymore (2013)
#32For those interested in this topic, I wrote a similar blog post on the geometric interpretation of the various trig functions, which also includes some similar diagrams for the hyperbolic trig functions: sinh, cosh, tanh, sech, etc. http://extremelearning.com.au/trigonometry-visualised/
A few sentences in. > "Sanskirt for 'chord' Sanskrit, you mean?
LOL! tx.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#33"goobledegook = e + 5.6. Wow you didn't know about goobledegook? Let me teach you about this revolutionary concept." I majored in mathematics and can say I've never heard of versine and have probably used it many times without knowing. I don't think everything needs a name.
I think the point of these was for when they read low-precision values out of a printed table and then multiplied them using slide rules. Even though the article doesn't say it, I can't think of any other practical reason to multiply by adding logarithms.
Slide rules are literally the physical embodiment of a log table (or several, if you had a multilog rule). You used them by physical addition.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#34"goobledegook = e + 5.6. Wow you didn't know about goobledegook? Let me teach you about this revolutionary concept." I majored in mathematics and can say I've never heard of versine and have probably used it many times without knowing. I don't think everything needs a name.
It kind of helps a non Mathie like me doing trig. But I'll ask fof one better: I would love an application that lets me plug in what I have (coords and angles), what I want, and for it to show me how to get it.
Here you go: https://www.geogebra.org/geometry
(Press the calculator icon for algebraic view)
Re: Obsolete trig functions and why we don't use them anymore (2013)
#35"goobledegook = e + 5.6. Wow you didn't know about goobledegook? Let me teach you about this revolutionary concept." I majored in mathematics and can say I've never heard of versine and have probably used it many times without knowing. I don't think everything needs a name.
versine clearly needed a name once when it was in common usage. As in, "Hey Greg, can you help me? I can't find this computation in these tables. --- Oh, try the versine".
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Re: Obsolete trig functions and why we don't use them anymore (2013)
#36atan2() is incredibly useful in game development. You can use it to determine the angle between objects, calculate the angle of a 2d vector, and other useful things. https://ryankubik.com/blog/atan2/
there is also sincos(), which is useful when you need both, such as building matrices.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#37I'm not that old, but I learned the haversine formula in a marine navigation class I took through (boy) scouts. Our instructor was a retired merchant navy officer who was somewhat upset that the curriculum didn't include it, and deemed that we should know it. My A-level (≈ AP) maths teacher was mildly amused that I knew it and digressed about log tables. We were (I believe) the last cohort to be issued log-tables, bu…
> given the choice in examinations between log-tables, slide-rule, or calculator, we all made the same choice
Students would benefit greatly if given a slide rule instead of an electronic calculator for their exams. The former is an effective teacher which viscerally reveals crucial insights, while the latter is pedagogically almost useless; using an electronic calculator to solve problems consists of nothing beyond punching keys and looking at the result, given as a disembodied string of digits entirely out of any context. The slide rule probably even ends up slightly more efficient for the type of problems students typically see in high school, after a bit of practice. Precision is more than sufficient.
Any assigned problem which needs a calculator would be more effective if the calculator were removed and the numbers involved were simplified to the point students could manage them mentally or with a trivial amount of scratch work.
Where electronic computers really shine is in their programmability, and for that students should be working with a full programming language and a real keyboard.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#38atan2() is incredibly useful in game development. You can use it to determine the angle between objects, calculate the angle of a 2d vector, and other useful things. https://ryankubik.com/blog/atan2/
In almost every context (certainly in game development) it is typically most efficient and numerically pleasant to avoid angle measures altogether and work in terms of vectors directly. To represent an angle, use a pair of numbers representing a complex number (optionally normalized to lie on the unit circle). If you want to reduce it to a single number (e.g. you have a large number of them you need to serialize to disk or send over the wire) use the stereographic projection.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#39Vers- is just from versus "opposite/against". But versine isn't opposite of sine, if anything it's opposing cosine. I too am curious this how this naming convention arose.
Wikipedia explains this clearly, https://en.wikipedia.org/wiki/Versine#Versine_and_coversine
Re: Obsolete trig functions and why we don't use them anymore (2013)
#40I'm not that old, but I learned the haversine formula in a marine navigation class I took through (boy) scouts. Our instructor was a retired merchant navy officer who was somewhat upset that the curriculum didn't include it, and deemed that we should know it. My A-level (≈ AP) maths teacher was mildly amused that I knew it and digressed about log tables. We were (I believe) the last cohort to be issued log-tables, bu…
It's also commonly used in astronomy to measure the distance on the sky between two objects: https://en.wikipedia.org/wiki/Haversine_formula
I could imagine these could be useful to be defined by computer libraries, as (see article) it would help reduce large reductions in accuracy for some calculations (e.g. by subtracting similar numbers, or wanting to calculate sin^2).