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Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. The first order ordinary differential equation initi

Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. The first order ordinary differential equation initial value problem d/dt y(t) = k y(t) ( b - y(t) ) can be use to model viral growth. Once it kept two crucial FedEx BoD members from walking out and saved the company. Similarly for the law of cosines for spherical triangles for finding great circle distances. Linear programming (LP) gets used right along for actual, genuine LP problems and also as a means of approximation for problems that are not linear. The problem of minimum cost flows is a special case of linear programming. If want to sort keys, e.g., for some positive integer n, if want to sort n numbers into ascending order by comparing numbers two at a time, then heap sort does that in worst and average case in O(n log(n)) and, thus is the fastest possible -- this is from a cute counting argument, the Gleason bound, A. Gleason. Statistics is important and parts of it are awash in math, not all of it trivial. The design and operation of the Webb telescope is awash in math.

mlyle 5y ago
> Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. Knowing a triplet ain't employing Pythagorean theorem. > [lots of following examples that are moderately deep applied math used in lots of skilled professions] Most people don't do this kind of work or analysis.
- graycat 5y ago
  > Knowing a triplet ain't employing Pythagorean theorem. 3^2 + 4^2 = 5^2 = 25 guarantees that the angle between the side length 3 and the side of length 4 is a right angle which is what the carpenter very much wanted to know. E.g., the sides might be 30 feet, 40 feet and 50 feet, e.g., for the foundation of a house, and presto, bingo the carpenter knows that the 30 foot side and the 40 foot side form a right angle, are square, which can be very important to a carpenter and not so easy to know otherwise.
  - mlyle 5y ago
    Yup, and knowing that having triangle sides multiples of 3,4,5 guarantees that it's a right triangle is not the same as employing pythagorean theorem. You know one triplet, and not why it works, or that e.g. it works for 5, 12, and 13 and 11,60, 61 as well. A whole lot of people know that measuring a bookcase corner to corner is a good way to square it up, too. But they may not be masters of geometry beyond knowing a rule of thumb.

mlyle 5y ago

> Uh, there is a carpenter with a Web site that uses the "3, 4, 5 rule", of course, the Pythagorean theorem. Knowing a triplet ain't employing Pythagorean theorem. > [lots of following examples that are moderately deep applied math used in lots of skilled professions] Most people don't do this kind of work or analysis.

graycat 5y ago
> Knowing a triplet ain't employing Pythagorean theorem. 3^2 + 4^2 = 5^2 = 25 guarantees that the angle between the side length 3 and the side of length 4 is a right angle which is what the carpenter very much wanted to know. E.g., the sides might be 30 feet, 40 feet and 50 feet, e.g., for the foundation of a house, and presto, bingo the carpenter knows that the 30 foot side and the 40 foot side form a right angle, are square, which can be very important to a carpenter and not so easy to know otherwise.
- mlyle 5y ago
  Yup, and knowing that having triangle sides multiples of 3,4,5 guarantees that it's a right triangle is not the same as employing pythagorean theorem. You know one triplet, and not why it works, or that e.g. it works for 5, 12, and 13 and 11,60, 61 as well. A whole lot of people know that measuring a bookcase corner to corner is a good way to square it up, too. But they may not be masters of geometry beyond knowing a rule of thumb.