AND the scales would intersect, not at -40, but at +75.7 (approximately. Precisely 1060/14).
Would it be less unexpected if said like this?: Complicated systems that include loads and loads of plumbing and tubes and containers and vessels of various sizes, be they evolved or invented, do better when they don’t operate around the freezing/thawing temperatures of the stuff they ingest?
[my bold]
Is this why internet service is so poor in Antarctica?
I had heard that Fahrenheit actually wanted his scale to have 96 degrees between ice brine and body temperature, because it’s easier to mark off a tube in 96 equal increments than 100. So his body temperature (or his wife’s, or whoever’s he was using) was a bit low, not high.
Why would 96 be easier than 100?
Because it has a lot more sub-multiples. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
100 only has 1,2, 4, 5, 10, 20, 25, 50, 100.
Or more explicitly: You can divide the initial length of your tube into thirds, and then you repeatedly bisect each of those intervals. Bisecting can be done more precisely than dividing into ten equal intervals, especially with the technology of the day.
Good point, but ISTM that the initial trisection would pose something of a challenge in itself.
Dividers can be used to get pretty accurate in dividing a scale that is several inches long. It’s only done once over the largest distance being divided.
To my knowledge no one has ever trisected an angle. My highschool geometry teacher was impressed by my ability to come up with proofs he’d never seen (I never paid attention in class so come test time I had to make shit up) so he set me the task of trisecting an angle. NTS I never did.
In fact there is a proof that it is impossible (for a general angle, using only a compass and straightedge). Your teacher was trolling you 
.
But trisecting a line segment is fairly easy.
I’ve trisected an angle. It’s quite easy, for instance, to trisect a 90º angle. But it’s impossible to trisect, for instance, a 60º angle (that is to say, to construct an angle of exactly 20º), using the standard tools.
But yeah, a straight line segment can be divided into any desired number of equal segments, using the standard geometric tools. And construction via geometric tools is irrelevant, anyway, because this is science, not math, and in the real world all precision is limited, anyway (which makes the mathematical constructions both less practical and unnecessary).
Can you put share that proof? Not challenging it; the terminology is that it’s impossible to trisect an arbitrary angle. Just can’t see the 90° proof in my head right now, 40 years after my last geometry class.
To trisect a 90º angle, just construct an equilateral triangle on each of the legs. It’s literally the easiest thing you can do with a compass and straightedge.
Fondly Fahrenheit’s brother?
In fact, whenever my wife or I take our temperature, it is just below 98.0; I think 98.6 is more of an ideal than an extremely precise point.
Was it Catch 22 where the sergeant gets all worried about the cows having a fever because they were not 98.6? (The joke being cows run at a different temperature)
I’ve taken the temperature of many people as a ‘test’ for covid. Their temperatures ranged greatly and even testing the same person 6 times in one hour gave a range of temperatures. Now, I realise thhere are many reasons for that (an amateur doing the test, innaccurate equipment, variation in people’s bodies, environment and people changing activities during the day). But these are the real practicalities of every day life when we say 98.6 - it is not very meaningful.
If you can trisect a line segment, you can trisect an angle too.
Take any given angle, from the apex, draw a circle using an compass. At the points of intersection of the circle with the lines, draw a chord. Now if you can trisect the chord (line segment) into 3 parts, you have also trisected the angle.
That relies on making parallel lines or eyeballing. There is no geometric way of guaranteeing that those lines are parallel. So I am not sure my Geometry teacher would have accepted that.
Try that out and report back.
It skips some steps, true, but constructing a line parallel to another line through a given point is a solved problem, so I think it is reasonable to skip those steps for clarity.
(Whether I would accept that answer if I was a geometry teacher would depend on whether we were at the point of taking previous proofs as “givens” in subsequent proofs – it is certainly reasonable for a working mathematician to do so).