Tag: proof

An Elegant Proof of the Pythagorean Theorem by a Former US President

By Anupum Pant

Abraham Lincoln, the 16th president of the United States, was probably a math whiz. Doesn’t it sound like an extremely rare combination of things a person could possibly be? – a president and a math whiz. And yet, he was not the only one. James Garfield, the 20th president, was very much into mathematics too.

Garfield wasn’t a professional mathematician. He was a president. But, much like Abraham Lincoln, he was very much into geometry! Before he went into politics, he wanted to become a mathematics professor.

While he was a member of the US house of representatives, five years before he was elected president of the US, he came out with a very elegant and unique proof of the Pythagorean theorem (yes, another one of those Pythagorean theorem proofs). Here’s how he did it with the help of a congruent flipped triangle…

Doing it with a piece of paper is really easy…

Pythagorean theorem proofFold a paper and cut 2 exactly same right-angled triangles out of it. Now, put them together as shown in the image here (click the image). Next, write down the area of the trapezium – (a + b) . ½(a + b) – 1

Now write the area of all the 3 triangles and add them. This is what you’d get – 2 x ½ ab + ½ c2  – 2

Since both these areas are same, just written in a different way, equate them and solve. You’ll end up with the Pythagorean theorem!

a2 + b2 = c2 

Or, simply watch the video to understand better…

The Old Tale of a Boiling Frog

By Anupum Pant

Background

The Frog in a pot is a very popular anecdote and you probably know about it. Still, if you don’t, it is about a frog that rests easy in a pot of water that is warmed slowly. Frogs normally won’t go into boiling water. They’ll jump out and keep themselves away from very hot water. But, if placed in a tub of water at normal temperature that is being heated slowly, according to the anecdote, they don’t react and end up getting cooked in the boiling water.

The story is used as a metaphor to tell a cautionary point about life. The moral of the frog story goes something like this – Letting small and seemingly harmless wrongs slip, could kill (or be bad for you).  It basically tells you to not be complacent about minor changes that usually seem harmless, but add up to something big/bad.

The video proof?

Scientifically, a bizarre video (not for the faint hearted) on Youtube claims to proves the frog tale. The guy in the video initially tries to put a frog in a pot full of boiling water. Of course it resists, and doesn’t go in. Later, when the frog is put into a pot full of water at normal temperature and is warmed gradually, the frog never tries to leave. It gets cooked in the boiling water. Just like the tale suggests.

Everything looks very convincing about the video experiment. Little details like placing the frog on a piece of insulator so that it doesn’t feel direct heat through the metal base, are also taken care of in the video. Also, the narrator sounds so convincing with all the science facts referring to how cold blooded animals react to temperature. They indeed do! I totally fell for it. Watch it below…

The video cuts in between and the water which was put on flame before starts boiling suddenly after the cut. Or brains tend to skip video cuts. In the boiling water is something that looks like a dead/cooked frog. If you watched it till the end, the video shows you that the dead frog wasn’t a real one. No frogs were harmed in the making of the video. Good.

But, that completely nullifies the point this experiment tries to make. A fake rubber frog being cooked in boiling water doesn’t scientifically prove the tale.

The Science

Unlike us, who maintain a constant body temperature, the frog being a cold blooded animal, its body will react to its surrounding temperature and will try to match it. But real scientific experiments have never been able to prove it. According to a very old experiment that was done in the 1800s, where water was heated at 0.002°C per second, the frog was found dead at the end of 2½ hours. Why do you think would the frog sit still for 2½ hours?

Modern scientists reject the old experiment which seems to prove it. You could place your trust in the words of a Harvard professor, Professor Douglas Melton. He says:

If you put a frog in boiling water, it won’t jump out. It will die. If you put it in cold water, it will jump before it gets hot—they don’t sit still for you.

Victor H. Hutchison, Professor Emeritus of Zoology at the University of Oklahoma also said, “The legend is entirely incorrect!”

Moral: don’t believe everything you see on the internet.

Hit like if you learnt something today.

Yeti Probably Does Exist + Fun Yeti Facts

By Anupum Pant

The search for Yeti, the mythical human-like creature that is assumed to have been living in higher elevations of the Himalayas, has continued for several thousands of years. Back in the days of Alexander the Great, during the 326 BC, when he was in the Indus valley area, he learned from the local people about the Yeti and expressed a desire to see it. The local people failed to bring it to him. Since then, several encounters have been reported and shoddy evidence has been produced, but till date, no one has succeeded in capturing the creature dead, or alive.

Proven Existence of Yeti

An Oxford university Genetics professor, Brian Sykes claims to have found a solid evidence that proves the existence of the Yeti. Moreover, according to him, it is a sub-specie of the brown bear. Specifically, an hybrid of the polar-bear and the brown bear.

After thoroughly studying two of the DNA samples (40 years and 10 years old samples) of hair from a mysterious animal found in Ladakh and Bhutan he said:

I think this bear, which nobody has seen alive… may still be there and may have quite a lot of polar bear in it. It may be some sort of hybrid and if its behavior is different from normal bears, which is what eyewitnesses report, then I think that may well be the source of the mystery and the source of the legend.

Interestingly, the DNA samples were found to be a 100% match with those coming from an ancient Polar bear that walked in Norway about 100,000 years from now. During those times a Polar bear was almost like a brown bear, the brown bear was yet to evolve.

– BBC

 Random Yeti Facts

  • Did you know, Yeti is also knows as the “Abominable Snowman” because the Tibetian word “Metoh-Kangmi” was mis-translated by a famous journalist as “dirty men in snow”.
  • There is a wildlife sanctuary in Bhutan that goes by the name Sakteng Wildlife Sanctuary which is dedicated to preserving the Yeti.
  • During the 1950s, the Nepal government issued formal Yeti-hunting-licenses which costed a massive $650 per Yeti. Otherwise, Yeti brings in a lot of business in Nepal. There are braded hotels and airlines named after the Yeti.(more at NatGeo)
  • Even in the virtual world, Yeti is a pretty popular creature. Games often like to include it as an easter egg. GTA San Andreas players claim that the Yeti can be found on the rocky faces of the Mount Chiliad at daytime. They say it is hard to see because it blends in with the mountain due to its color. GTA V players have encountered a similar beast, the BigFoot.