What is the most beautiful equation you have ever seen?


This is supposed to be one of the Google interview questions in the book Are You Smart Enough to Work at Google. I immediate thought of the equation e^(i*Pi) = -1. The Euler’s equation is a simple and neat equation that is also quite important for engineering students. But it is “beautiful’ to me because of a beautiful memory I have related to this equation.

It was on a Saturday afternoon at home when out of nowhere someone asked me the question “what is e to the power of i pi”. I did some mental calculations (because I couldn’t remember the equation off-hand) and answered -1. He smiled and said “you are smart”. I’m not sure if being able to answer a simple question like this is considered as smart, but it is perhaps one most enjoyable experience to have geek talks with someone who shares the same interests and is also a geek like me. It always a sometimes a very scientific or “geeky” thing can be made beautiful because of a wonderful memory shared with an important person in life.

Beauty is really a subjective matter. For me beauty is something that relates to our memory, it is unique and personal because no two people have the same memory, even if it’s of the same event.

I was surprised to see that the exact same equation is actually the canonical Google answer to this question. An interesting and amusing answer given by Richard Feynman is U = 0. His argument is that everything in the universe can be reduced to this equation. Euler’s equation, Einsteins’ equation, Schrodinger’s equation all add up to 0. Of course he was half-joking, but that is as simple as an equation can get.

Nikola Tesla in Colorado Springs

I’m deeply impressed by this photo. It depicts a true genius inventor with his crazy invention.

Nikola Tesla in his lab in Colorado Springs and what he considered as his best invention, the Magnifying Transmitter transmitting millions of volts of electricity.

The 4Cs for evaluating ideas

Consider the 4Cs when evaluating an idea. An excellent idea needs to satisfy all four aspects.

Clarity – Does the idea clearly meet a need or solve a problem?

Content – Does it have substance?

Creativity – Is it original and valuable for your audience?

Craft – Is it professionally crafted?


From the book IdeaSelling: Successfully Pitch Your Creative Ideas to Bosses, Clients & other Decision Makers.

DARPA Scientists Create Superfast Wi-Fi That Attaches Information to Light Beams

Terabit data rate using twisted light. This is the topic for my optical communication term paper. I like the last part of the video:

“Imagine downloading all of the Star Wars films in a blink of the eye, even if we’re only going to watch three of them.”

Our augmented selves: The promise of wearable computing


Our augmented selves: The promise of wearable computing

Comic: Why Nikola Tesla was the greatest geek who ever lived

A fantastic and funny comic explaining why Nikola Tesla was the greatest geek who ever lived

Continue reading at

M10’s ultra small flexible biometric health sensor

MC10’s ultra small biometric health sensor can be worn on the body like a transparent bandaid. This sensor can measure your body temperature, hydration etc. The company is now working on wireless power and data communication with smartphones. This sensor looks amazingly small and thin, could it become the next generation “invisible” wearable sensor?

Understanding different roles of BLE devices

I was really confused at first about the different roles devices get as stated in the BLE protocol stack. After spending a lot of time painstakingly read through the CC2540 BLE software developer’s guide by TI, I got a clearer picture of the different roles involved.

Central and Peripheral 

These roles come under the GAP layer, which is responsible for the discovery and link connection between devices.

Peripheral: Sends out advertisements to inform central devices that it is ready for connection.

Central: Scans for advertisements from peripheral devices and initiates connections

There are 2 other roles in the GAP layer – Broadcaster and Observer. Broadcaster is like peripheral that sends out advertisements but not connectable. Observer is like central which scans for advertisements but cannot initiate connections.

Server and Client

These 2 roles belong to the GATT layer, which is used by applications for data communication between two devices that are already connected.

Server is the device that has the data to be read or written by the client.

Client is the device that sends out request to read or write data from the server.

The important thing is that these 2 roles are completely independent from the GAP roles (central/peripheral). So  a central device can be a server or a client, a peripheral device can also be a server or client.

A client can be configured to receive notifications from the server, so it doesn’t have to send out request to the server every time it wants data. When the server has some data to be sent, it will automatically notify the client of the data value without any request.

In iOS6, the Core Bluetooth framework allows an iPhone with BLE to be either a central or a peripheral device. The framework allows a central to be connected to multiple peripherals, and a peripheral can also be connected to different centrals at the same time. (WWDC 2012 Core Bluetooth 101).

Here is a very useful presentation explaining how BLE works, especially on the details of the different roles.

Homemade adjustable DC power supply

I was at my parents’ house this holiday and I wanted to power some small electronics project but found myself without a DC power supply. So I decided to build my own using a simple LM317. The input is a 12V, 1A wall wart, adjustable output voltage from 1.7V to 10.3V. This should be able to power most electronic projects that require low voltages.

1 2 3 4 5