Comments by Paul

  • Paul's dead reckoning robot

    Paul's dead reckoning robot

    - 19 August 2015

    For anyone interested in building a robot like this, our new A-Star 32U4 robot controller includes most of the electronics shown here, on a single PCB. So if you use that, you can skip the breadboard and directly wire your batteries, motors, and sensors to the controller.

  • Paul's dead reckoning robot

    Paul's dead reckoning robot

    - 20 July 2015

    I have not made a wiring diagram (need to learn Fritzing!), but I still have the robot, so if there are any connections that are not clear in my post, I would be happy to check them for you.

  • Math on the Pololu website!

    - 27 June 2014

    Ben wanted me to post the details of the Gaussian integral, so here we go.

    It's simpler to think about the full integral from ``-oo`` to ``+oo``. Let's give that a name:

    ``lambda = int_-oo^oo e^(-x^2) dx``.

    Then, instead of trying to compute ``lambda``, we work on ``lambda^2``:

    ``lambda^2 = ( int_-oo^oo e^(-x^2) dx )^2 = int_-oo^oo int_-oo^oo e^(-x^2) e^(-y^2) dx dy``.

    We note that ``e^(-x^2) e^(-y^2) = e^(-(x^2+y^2))`` and rewrite in polar coordinates:

    ``lambda^2 = int_0^oo e^(-r^2) 2pi r \ dr``.

    Luckily, that integral is easy, since ``d / (dr) pi e^(-r^2) = - 2 pi r \ e^(-r^2)``:

    ``lambda^2 = - [ pi e^(-r^2) ]_0^oo = pi``;

    ``lambda = sqrt(pi)``.

    Finally, since the Gaussian is an even function, our desired integral is just half of that value:

    ``int_0^oo e^(-x^2) dx = sqrt pi / 2``.

  • Pocket-sized USB charger adapter

    Pocket-sized USB charger adapter

    - 6 March 2014

    Thanks for the nice feedback, and please let us know when you post more projects!

New Products

Wixel Shield for Arduino, v1.1
DRV8880 Stepper Motor Driver Carrier
Addressable RGB 8x8-LED Flexible Panel, 5V, 10mm Grid (APA102C)
75:1 Micro Metal Gearmotor with Extended Motor Shaft
5:1 Micro Metal Gearmotor HPCB
Addressable RGB 16x16-LED Flexible Panel, 5V, 10mm Grid (APA102C)
Addressable RGB 8x32-LED Flexible Panel, 5V, 10mm Grid (APA102C)
MP3 Trigger V24
5:1 Micro Metal Gearmotor MP with Extended Motor Shaft
700:1 Sub-Micro Plastic Planetary Gearmotor 6Dx21L mm
Log In
Pololu Robotics & Electronics
Shopping cart
(702) 262-6648
Same-day shipping, worldwide
Menu
Shop Blog Forum Support
My account Comments or questions? About Pololu Contact Ordering information Distributors