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Saturday, May 20, 2017

Angling Mathematics: Fishing For Complementary Angles

      Our late-spring trip along the North Platte River from Waterton Canyon to Deckers, Colorado, and on to Wellington Lake, was filled with angles and anglers. According to the link cited above, 


  "There are physical properties associated with the bending (refraction of light) which have significant effects on what a trout could possibly see.  The trout’s world consists of a window, the diameter of which is determined by a thing called the Snell’s equation."



    "In simple terms the window is 2.26 times as wide as the trout is deep. So it can clearly see things on the surface over a wider area the deeper the fish is. At one meter the fish can clearly see things on the film in a 2.26 meter wide circle above its head."


      "Many angling writers have made much of this, because a relatively small increase in depth radically changes the size of the window. At 0.5 meters the window has a diameter of 1.13 meters, but at a depth of a meter that window grows enormously to 2.26 meters across. If you take the area of the window the results are all the more dramatic. At 0.5 meters depth the area of the window is 1 square meter, at one meter in depth that window jumps to 4 square meters. Double the depth and you effectively quadruple the size of the window."

      Ah, look at this sky window near Wellington Lake.




       The term angler derives from one who uses an "angle, or, originally "angel," i.e., fishhook for fishing with a line.



     
     A bit of both angles and angels might be involved in angling mathematics.



       Much better angling earlier in the week than on May 18 during the intense Colorado snowstorm. . .




      Big flakes abound in Colorado this month ;-).





      Are you an angler?

Fishing for complementary angles,
Steph




32 comments:

  1. So, to paraphrase Jonathan Livingston Seagull, "The trout sees the farthest that swims the deepest"?

    Something's fishy here. "Snell" is defined as "a short line of gut or horsehair by which a fishhook is attached to a longer line". So, Snell's Law for fish ought to be, "Stay away from the snell!"

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  2. Just livestreamed Oprah Winfrey's speech as Smith's commencement speaker. Some good, inspiring moments, aside from the burning bodies on a plane part. Many Zoës, Sarahs, and Chloës; most graduates looked happy and dazed. ;-) The Ada Comstock graduates (non-traditional age students) always inspire. . .

    John Brady, my mineralogy-petrology professor received a teaching award. His teaching philosophy is to step away more so students do their own learning. His was the "Wallpaper Sample" final exam for symmetry in crystals.

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  3. I only went fishing once, on a beautiful lake in the Adirondack Mountains. I caught a trout in a few minutes, but was not pleased by the hook removal and head slamming (fish not mine) process, so I tied a noose in my line for any fish in fits or facts of depression.

    Deeper waters also have the advantage of more consistent temperatures, and safety from above water predators. A favorite memory is a beautiful bald eagle grabbing a fish too near the surface at the appropriately named Snag Lake in Lassen Volcanic Park.

    Did you see this article on glowing mouse heads?

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  4. Fascinating article, eco. Thanks for sharing it.

    My brain could use some good dishwashing about now. I have been tutoring kids in calculus, algebra, and SAT prep all week and over this weekend; certainly that warrants lots of glymphatic flushing.

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    Replies
    1. Great memory from Snag Lake in Lassen, too.

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    2. The eagle's wings actually made a lot of noise while flying, definite contrast with other raptors I've seen - hawks, owls, golden eagles or peregrines.

      At first I thought this is an evolutionary disadvantage, though the first three primarily dine on ground critters we find annoying, mice, voles, rats, snakes, poodles; and peregrines feed on other birds. Silence is a definite advantage.

      Fish likely can't hear the wing flaps, but I also note that bald eagles also steal from others and perhaps the wing noise is to frighten other animals. I noticed smaller birds in the trees were quite disturbed by the flap.

      I haven't seen any reference papers on this, but I find the thought amusingly metaphoric: the noisiest, bald(ing) creature scares his competition away with his bluster and ultimately steals the prize by snaring those under water.

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    3. Ahem, Maizie is part poodle. . .

      Interesting hypothesis, though, eco.

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    4. Apologies to Maizie, I grew up with a poodle. Lots of barking.

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    5. Apology accepted, eco. Maizie only barks at the mail carrier and UPS/FedEx folks or if someone is trying to break in to our house. She's not at all yappy.

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    6. I had some clients who lived in a double wide trailer on 40 acres west of Phoenix. They bred and sold mastiffs, which only barely tolerated my presence on "their" land. The owners told me that one day while they were out the UPS guy came with a package. The dogs got so excited/ enraged they tore a hole through the trailer walls; fortunately the UPS driver got safely into his truck in the nick of time. No more deliveries for them.

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  5. Replies
    1. Of course, until they can predict cloud cover on earth, it doesn't matter how well they can map every lunar hill and valley.

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    2. True. I am betting on central Wyoming or western Nebraska, though, for August 21st.

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  6. Replies
    1. I didn't know about cell phone screens being made of sand.

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  7. Replies
    1. Perhaps Highway nOne.

      It is very pretty, though I consider where the landslide happened to be not nearly so nice as parts north.

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    2. Highway nOne is great, eco.

      Driving along Route 1 from near Humboldt State U in Eureka to the Oregon border and northward through Coos Bay and Seattle to Port Angeles to a ferry to Victoria and Vancouver was remarkable. The Humboldt Bay oysters were fabulous, friends in Coquille were welcoming, Mt St Helens was a trip, and the scenery stunned at every turn.

      I returned several years later to take in the beauty of the redwoods and Crater Lake,OR. An extant ocean would definitely add to Colorado!

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  8. Replies
    1. Wait. The study involved 149 patients with 15 different cancers. 60% had no response. Big news for Merck, maybe.

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    2. Interesting to hear your thoughts, jan. My friend, a cancer researcher, was quite excited about it. I'll admit to passing it along without an in-depth reading.

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    3. Ok, sure, I can see how this might be exciting to a researcher. But I think the jury is still out on the clinical significance. And when you stack those trial results and the $9000/dose price tag against the numbers of people with lung, colon, ovarian and uterine cancers, etc, it seems less impressive.

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  9. I asked a librarian about a book on Pavlov's dog and Schroëdinger's cat.

    She said "It rings a bell but I'm not sure if it's on the shelf or not."

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  10. Smith College released this video on drones and sea turtles yesterday. Thought I'd wait until today to post it ;-).

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  11. I recently discovered Undiscovered -- a podcast about the backstories of science, a spinoff of Public Radio's Science Friday, which may be of interest to readers of this blog.

    We've previously discussed looking for meteorites. This segment deals with doing that in Antarctica.

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    Replies
    1. It's a cool concept.

      I enjoyed the meteorites in Antarctica piece.

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  12. Replies
    1. Yeah, but wait until they hear what happened to Laika...

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  13. New post on "Track Lighting: Dinosaur "Dance Floor" in Bolivia -- Over 5,500 Footprints" is now up.

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