Recent content by Charles Link

  1. Charles Link

    Why Does Snow Pack Better Near the Melting Point?

    The above is a photo of a 3'8" "snowlady" I made today, December 7, 2025, in Chicago, along with the snowman that is still there from November 30 that now measures 4'4" tall. Packing conditions were fair today with temperatures around 32 degrees with no sunshine.
  2. Charles Link

    Undergrad Trigonometry problem of interest

    Some of it depends upon who the audience is. If you have a construction worker building something, he'll know immediately what a 90 degree angle is, but if you tell him you want it to be ## \pi /2 ## radians, good luck. LOL
  3. Charles Link

    Undergrad Trigonometry problem of interest

    Sometimes it's simpler to use degrees rather than radians for the measurement of angles.
  4. Charles Link

    Announcement PF Member Awards 2025 Coming Soon!

    One of my favorite times of the year. If I'm lucky I may even get on the ballot, but it's a lot of fun in any case. :)
  5. Charles Link

    Why Does Snow Pack Better Near the Melting Point?

    The above is a photo of a 5'0" snowman I made today, Sunday Nov. 30, 2025 in Chicago. We had about 8" of snow yesterday, but I had to wait until early this morning for the temperature to get above 32 degrees for any good packing. The snow packed fairly well with temperatures at 33 degrees for...
  6. Charles Link

    Undergrad Trigonometry problem of interest

    @neilparker62 This parameterization method is really kind of simple once you figure it out, and it's based on solutions using the quadratic formula, that for both the plus and minus solutions, the square root of ## b^2-4ac ## will be rational, making for two rational solutions, one of which...
  7. Charles Link

    Undergrad Trigonometry problem of interest

    I thought @hutchphd 's of post 49, (see also post 52) was simpler. I think this latest (post 73) I would call "a" most efficient solution, but not "the" most efficient. :) Edit: Notice it does indeed give the general result that ## x^2=(a^2+ab+b^2)/3 ##.
  8. Charles Link

    Announcement RIP Vanadium 50

    He was one of the smarter ones on here. We will miss him.
  9. Charles Link

    Why Does Snow Pack Better Near the Melting Point?

    @DaveC426913 I am still waiting to see most of the geese fly south. I don't think most of them have gone south yet. If they did, I missed them.
  10. Charles Link

    Why Does Snow Pack Better Near the Melting Point?

    The above is a photo of a 4'6" snowman that I made today, Monday 11-10-25, in Chicago. It is the first one for this season. We had about 3" of snow overnight, but at first the snow was too cold to pack. I waited a couple hours until things warmed up above freezing around noon, and it packed...
  11. Charles Link

    Undergrad Why use Stefan's Law to measure temperature?

    In that case, one would need additional spectral detail, such as measuring with two or more bands.
  12. Charles Link

    Undergrad Why use Stefan's Law to measure temperature?

    I was able to use it to determine the temperature of a calibration blackbody source with known aperture size at close range, ( distance of one foot). In general, bandpass measurements with the Planck blackbody function are necessary.