This could be big.
But, only in bank employees, sadly.
Maybe weâll all be tripping
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This came up in my feed today. An interesting approach to factoring quadratic equations. It claimed to be simpler than usual methods and remove âguess and checkâ. It actually ended up being pretty clever.
4 minute video, first half is âinspirationâ, second half shows the method:
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It doesnât seem any easier than using the formula. More steps, actually.
The point is, you donât need to memorize a formula for it.
True, but one needs to memorize the process.
And, one can always solve the formula if one forgets. Solve it enough times, one will remember the formula.
Also, this method only works when A = 1. Is there an âeasy wayâ to solve when A <> 1? I WANT MY 2 MINUTES BACK!
Nice that B was an even number in his example. Suppose it is 7 (keep C = 12).
Now,
step 1: let a = factor 1 = 3.5 - u; let b = factor 2 = 3.5 + u
step 2: multiply a and b; ok, 3.5^2 - u^2 = 12. Great, this isnât difficult at all! Lucky me that squared factors of 5 make this 3.0 * 4.0 + 0.25 = 12.25. So u^2 = 0.25. and u = ± 0.5.
So, a = 3, b = 4.
Easier to list the factors of C, see which ones add to B. One will note that starting from {1, C} and increasing the first factor, the sums get smaller. If you go past B, there are no rational solutions.
The YT video did say it was a âdifferent wayâ not easier, so, this belongs in the âho-hum scienceâ thread.
Proof of odd squared factors of 5: Let natural number A = 10 * B + 5.
A^2 = 100 * B ^ 2 + 100 * B + 25.
= 100 * (B) * (B + 1) + 25
= (10 * B) * ((10 * (B + 1)) + 25.
10 * B is the factor of 10 below A, ((10 * (B + 1)) is the factor of 10 above A.
QED
Divide by A first?
One nice thing about his method is that it also finds irrational solutions, unlike guess and check.
Iâm not claiming its groundbreaking or anything, but I can certainly see it making intuitive sense to kids, as opposed to memorizing the quadratic formula or completing the square.
Factoring quadratics is for math students .
Well, it is a way for kids to think, âYeah, that formula works every time; I think Iâll use that instead.â
This method is completing the square.
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Agree. It is.
interesting. do they offer anything to do differently to avoid slips/falls?
That tooth in eye transplant.
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Nobel time! Found some cool explainers on the nobelprize.org site:
https://www.nobelprize.org/all-nobel-prizes-2025/ Check out the popular information links.
Congrats to my colleagues here at UCSB!
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Why Is This Lake âBurpingâ?
For hundreds of years, people who have lived near Seneca Lake in upstate New York have reported hearing loud booms coming from the water. No one is exactly sure why.
By David Andreatta
Jim Mead was fishing 30 years ago on Seneca Lake, the largest of the Finger Lakes of central New York, when he experienced what he believes was the phenomenon that has confounded the region for hundreds of years.He recalled leaning over the side of his boat and seeing something in the water about 20 feet away. A large bubble, which he described as three feet in diameter, shot up from the waterâs depths and exploded at the surface with a loud bang.
âIt made this really deep boom sound,â said Mr. Mead, 66, who captains pontoon boat cruises to Finger Lakes wineries. âIt didnât make much of a water splash, strangely, but it was a big boom!â
The mystery may now finally be solved by researchers who last month plumbed the depths of Seneca Lake to test for methane and other geological gases that might prove once and for all what has long been suspected: The lake is burping.
âItâs a longstanding mysterious phenomenon that no one knows the answer to,â said Tim Morin, an associate professor at the State University of New Yorkâs College of Environmental Science and Forestry and one of three principal investigators of the sounds. âWe think we know what explains it. Now weâve got to prove it.â