## 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…

Fold 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 c – 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…

## A Few Things About Sloths Everybody Should Know

###### by Anupum Pant

A few days back, on 20th October, Sloth Day was celebrated all around the world. You’d be thinking, what is so good about these strange animals, that makes people have a special day around them. Well, in that case, you need to read this.

### What are these creatures?

Sloths are slow animals that make even cows look extremely active. They are so slow that they are almost stationary and algae grows on their hair. Most of their life is spent on trees hanging upside down. They hang on trees to protect themselves from the predators on the ground. Their bodies are so well engineered to stay inverted that the hair on their bodies, is oriented in the opposite direction – growing from stomach to back (This helps them to stay dry by draining water easily). Even dead sloths have been know to retain their grip and remain suspended after death. They come down only around once a week to excrete. They eat, sleep, travel, find partners, mate, give birth and even raise young ones in the canopies.

Although sloths might seem gross, creepy and unseemly, they really aren’t that bad. Sloths are sweet looking [1] [2] [3] animals (especially their babies, they are adorable) who can also swim efficiently and move wisely. We can definitely learn a lot from them.

### Their diet is unbelievable

Sloths eat only leaves throughout their lives. They chew leaves slowly like cows to extract whatever nutrients they can. Sloth intestines are also adapted to extract the maximum out of their poor quality food, they are unusually long. They often like to shift to a different kind of leaf after a day or two. This balances their nutrient intake. Humans couldn’t possibly survive on a leafy salad diet for a very long time.

To save energy, sloths drop the temperature of their bodies at night. Even their bodies have more bones than muscles to prevent wastage of energy through muscular movement. After the Orangutan they are the most energy efficient animals.