41–50 of 144 posts
atan2() 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/
Why game development? It's useful everywhere! I have never found a genuine usage of atan(), it's always atan2() that is natural to use.
Earlier quoted context omitted.
I don't agree at all. This happens all the time. For example, electrical engineering has f , ω , and s , all only differing by basic factors of 2 π or i . As far as I can tell, the main reason this gets done is to give commonly recurring quantities single symbols, to reduce errors in lengthy calculations. When those recurring quantities are meaningfully different, in ways that help prime one's intuition, that's all t…
As an electrical engineer you'll typical use f, ω, and s, in different contexts and you'll learn each of those contexts separately. f: consumer electronics ω: circuits s: frequency response Having multiples of terms for each is definitely a hindrance to education. It makes switching between each use a mental headache.
Perhaps it's just my unconventional education (see username), but when I'm doing something like filter design, I really do end up using all of those at once. I'll do the on-paper design portions with s, the computational section of the design with ω, and then when I build the thing to test it, the scope or spectrum analyzer read out in f (if I'm lucky). So they're genuinely all there at once!
haversine is incredibly useful when you're doing quick distance calculations between points on the Earth though...
I'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…
I learned it while reading the Wikipedia article Slide Rule, it mentions that two math educators David B. Sher and Dean C. Nataro invented a Prosthaphaeresis slide rule in 2004 - it's what a slide rule may look like in an alternative universe. Unfortunately, I still haven't seen it - I couldn't find the original paper, it doesn't seem to have a DOI, can't use Sci-Hub.
I'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…
I'm also mildly amused that the author failed to mention the hyperbolic functions, of which there is one for each of the regular circular trig functions
Earlier quoted context omitted.
It always bugged me that secant is 1/cosine, cosecant is 1/sine, and cotangent is 1/tangent. Like what does co- mean? Trigonometry never really clicked for me. I can remember the formulas and such, but I never really understood what they meant. It was an exercise in remembering but never knowing.
The prefix 'co-' stands for complementary. Two complementary angles add up to 90°. The cosine of a angle is therefore the sine of its complementary angle, etc. For the secant and tangent, it originates from the geometry of the unit circle. The first image in the article explains it well.
I'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…
I recently learned about the existence of the Prosthaphaeresis algorithm [0], an even more ancient and obsolete trigonometric calculation technique. It allows you to use a trig table to do calculations when you don't have a log table. To calculate a x b , find arccos( a ) and arccos( b ), then use the product-to-sum formula: cos( a ) x cos( b ) = 1/2 x [cos( a + b ) + cos( a - b )]. For example, to calculate 42949672…
If you want to multiply two numbers, you can treat them as rotations, take the logarithm of each (i.e. find the angle measure), add the two, then take the exponential.
I'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…
atan2() 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/
> atan2() is incredibly useful in game development Why game development? It's useful everywhere! I have never found a genuine usage of atan(), it's always atan2() that is natural to use.
[ x, y ] ↦ [ atan2(y, x), π/2 − 2 atan(√(x² + y²)) ]
But atan per se comes up all over the place if you start doing much work with angle measures.
"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.