## Smart Fallacies: i squared equals to 1, 1 equals to 2 and 3

This mathematical fallacy is due to a simple simple assumption, that $-1=\dfrac{-1}{1}=\dfrac{1}{-1}$ . Proceeding with $\dfrac{-1}{1}=\dfrac{1}{-1}$ and taking square-roots of both sides, we get: $\dfrac{\sqrt{-1}}{\sqrt{1}}=\dfrac{\sqrt{1}}{\sqrt{-1}}$ Now, as the Euler’s constant $i= \sqrt{-1}$ and $\sqrt{1}=1$ , we can have \$ \dfrac{i}{1}=\dfrac{1}{i}… Continue reading

## 0.999…=1?

There is a clinical fallacy which proves 0.999… =1. First we assume the repeating decimal n=0.9999…                      …(i) Then, 10n= 9.9999…                      …(ii) Subtracting equation (i) from equation (ii) we get 9n=9 Thus, n=1. It proves the post title. But how is it possible? Two different real… Continue reading

## Four way valid expression

People really like to twist the numbers and digits bringing fun into life. For example, someone asks, “how much is two and two?” : the answer should be four according to basic (decimal based) arithmetic. But the same  with base three (in ternary number system)… Continue reading

## Tunnel through the Earth

What if we make a tunnel through the earth and drop a ball or any other body into it? How would the gravity behave on the ball, and , will the ball pop-up on the other side? If yes, then how much time will it… Continue reading

## Happy Holi! : The Village Tour

Holi, the festival of colors, was celebrated this year on 27th and 28th of March all over India. I decided to move to my own village, Kasturwa and then to Surya’s Village, Shiv Patti, on this occasion. Here are some images from the events  taken with my Nokia device, which I thought were worth sharing. Happy Holi!

# Rangoli

Rangoli is one of the most beautiful arts made on festivals in Uttar Pradesh. The below one isn’t that good, but fair enough to be shared.

# Photo One: Friends

This is a photo taken at nearby market of my village. Left to right we are, Vishal Shahi, Suryakant Tripathi, Me, Raman Pandey, Atul Pandey & Deepak Kumar.

LOCATION: Chaura Khas, Kasturwa

# Photo Two: Tripathi Brothers

Now, here are the Tripathi brothers: Shivakant, Surya and Chandrakant. Very nice pic, I’d say.

LOCATION: Shiv Patti

# Photo Three: Colorful me

I am resting after a tiring play of colors. (I am right. )

LOCATION: Shiv Patti

# Photo Four: Drumming Surya

Once again, Suryakant tries to play a drum. A photo with some kids from his village.

LOCATION: Shiv Patti

# Photo Five: Regional Songs

The “Faguwa Toli” singing the regional songs.

LOCATION: Shiv Patti

# Photo Six: Kidding?

Surya and Shivakant with a bunch of kids.

LOCATION: Shiv Patti

# Photo Seven: Aftermath

Getting fresh after the Holi day : here is a photo of me – trying to view the Sun into the angle between fingers and thumb.

Here again,

PS: Surya (a.k.a. Suryakant Tripathi ) is one of the team members.

## My Five Favs in Math Webcomics

Cartoons and Comics are very useful in the process of explaining complicated topics, in a very light and humorous way. Like:

Source of These Cartoons
Here my five most favorite math-webcomics sites. (Click on images to visit them.)