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iThinkOfYou
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Playing with a heart! Literally! 
It is all about finding the center of mass!
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Imranovi
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How to make a Celtic Heart Knot Necklace, a perfect summer accessory. : http://goo.gl/LcoItd
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A colleague of mine, Tadashi Tokieda, has a nice mathematical demonstration appropriate for St Valentine's Day. Years ago, I entertained my then children (by which I mean that they are grown up now but I have more children) with cutting Mobius strips in half, so I was familiar with some of this. But Tadashi takes things a step or two further. If you're short of time, then I'd recommend starting at about the one-minute mark. (The video is two minutes and 37 seconds.) And if you're really short of time, you could start at 1:40 and cut right to the chase. But it's better if you watch the whole lot.

In an email to me, Tadashi made the following remark, which I lack the knowledge to understand, but which I include for the benefit of those less ignorant than I am: "What you are getting at the end is R^2 blown up at a point twice successively then sliced along the exceptional divisor." Perhaps someone can explain this to me.
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Engagers Showcase Circle, April 17, 2014

If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.

This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. Two of the posts below attracted too much engagement to be usable for the circle, but I am including links to them for completeness.

Everyone mentioned below is also included in the circle.

Adding cubes
https://plus.google.com/101584889282878921052/posts/WqimoVTZWL3

Flower and snail shell (reshared from +Ralph Reichert)
https://plus.google.com/101584889282878921052/posts/5st1n4VBMh5

April Fools' Day
https://plus.google.com/101584889282878921052/posts/Mxa1TNjYo4r

“Trinity” by Jen Stark
https://plus.google.com/101584889282878921052/posts/gfRheBovSZU

Hyperbolic honeycombs (reshared from +Roice Nelson)
https://plus.google.com/101584889282878921052/posts/59yPx8yoFbu

Coxeter—Conway friezes
https://plus.google.com/101584889282878921052/posts/4XvYb9biaLp

Triple helix staircase (reshared from +Romain Brasselet)
https://plus.google.com/101584889282878921052/posts/SRJ7CqGNrtL

Which airport is closest to you?
https://plus.google.com/101584889282878921052/posts/FxxdDb6orPy

“Spinning Cosmos” by Paul Friedlander
https://plus.google.com/101584889282878921052/posts/RjnVfRhBPmZ

Strč prst skrz krk
https://plus.google.com/101584889282878921052/posts/h87PZWs2MSb

Mersenne primes and perfect numbers
https://plus.google.com/101584889282878921052/posts/cLWBTddiSyy

“Urge to fly” by Hermin Abramovitch
https://plus.google.com/101584889282878921052/posts/j2K97AvLvAo

Keeper of Time (reshared from +Michael Quinn)
https://plus.google.com/101584889282878921052/posts/QnaHrgKjsUU

Seven mutually touching cylinders (reshared from +David Richeson)
https://plus.google.com/101584889282878921052/posts/QWEzmvFkL4x

A present from a student
https://plus.google.com/101584889282878921052/posts/Lt2UyPkpGNo

Campus photo (reshared from +University of Colorado Boulder)
https://plus.google.com/101584889282878921052/posts/WQqVVNLoq3e

As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!
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Engagers Showcase Circle, March 29, 2014

If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.

This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. My most recent post will be included next time.

Everyone mentioned below is also included in the circle.

Happy Pi Day!
https://plus.google.com/101584889282878921052/posts/74oomcTuJoV

Sierpinski sponge (reshared from +David Roberts)
https://plus.google.com/101584889282878921052/posts/ZKUreVJfWxo

Cloud Gate (reshared from +Christian Cable)
https://plus.google.com/101584889282878921052/posts/XGRNqbbBjgE

Continued fractions
https://plus.google.com/101584889282878921052/posts/2mbZvUrewmC

Food maps
https://plus.google.com/101584889282878921052/posts/BKMgJ6Wzfiy

Neptune's Lament (reshared from +Paul Haworth)
https://plus.google.com/101584889282878921052/posts/1AHZMatxm8J

Escher's “Ascending and Descending”... in Lego
https://plus.google.com/101584889282878921052/posts/9XJsanAguNC

Dead Horse Point State Park (reshared from +Tom Malloy)
https://plus.google.com/101584889282878921052/posts/edKVZ8NqAW4

It's the Chicken from Hell! (reshared from +Chad Haney)
https://plus.google.com/101584889282878921052/posts/2tc9WchRABJ

Derangements, or how everyone got the wrong homework back
https://plus.google.com/101584889282878921052/posts/Bjb3CvDYBwx

Snowy La Sal Mountains (reshared from +Tom Malloy)
https://plus.google.com/101584889282878921052/posts/8tiW4gbzVrX

Multimove chess
https://plus.google.com/101584889282878921052/posts/Vu3vfhGfwuh

As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!
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Engagers Showcase Circle, March 20, 2014

If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.

This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. I ran out of room, so my most recent posts will be included next time instead.

Everyone mentioned below is also included in the circle.

Michelangelo and the Jordan curve theorem
https://plus.google.com/101584889282878921052/posts/UN8TetdX48V

The Kelpies
https://plus.google.com/101584889282878921052/posts/M6aWXwu6zES

Antoine's necklace
https://plus.google.com/101584889282878921052/posts/4anPfBNTyjX

The Farey-Ford tessellation
https://plus.google.com/101584889282878921052/posts/GrZP3ajnRGU

Alien Garden (reshared from +Kevin Clift)
https://plus.google.com/101584889282878921052/posts/j55RpNfocNA

Between a rock and a hard place
https://plus.google.com/101584889282878921052/posts/WGNdNFneW1u

Alan Turing: a universal Turing machine?
https://plus.google.com/101584889282878921052/posts/MUjAnVtL7hb

Visual artist Aliza Razell
https://plus.google.com/101584889282878921052/posts/hbd3e6U1fhS

Beet it (reshared from +Laura Ockel)
https://plus.google.com/101584889282878921052/posts/U7RjV31mM7W

Chess played on a sphere... and other animals
https://plus.google.com/101584889282878921052/posts/LGXUE73Z3Mo

Pass 'Em On
https://plus.google.com/101584889282878921052/posts/iFCQcXfhNdD

Arizona sunset (reshared from +Debashish Samaddar)
https://plus.google.com/101584889282878921052/posts/CR1yJ48g8CW

The inside of my fridge, through Glass
https://plus.google.com/101584889282878921052/posts/SQK6KoFL2rm

Batmobile 1?
https://plus.google.com/101584889282878921052/posts/aV43AZenAd9

Mary O'Malley ceramics (reshared from +Carl Niclas)
https://plus.google.com/101584889282878921052/posts/dX4UYXh4nXn

As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!
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Engagers Showcase Circle, March 4, 2014

If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.

This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. I ran out of room, so my eight most recent posts will be included next time instead.

Everyone mentioned below is also included in the circle.

Robert Wadlow
https://plus.google.com/101584889282878921052/posts/442C6iBpXpT

Blanchard Springs Park (reshared from +David D)
https://plus.google.com/101584889282878921052/posts/ZJmBps8sgSN

Pascal's triangle and the number e
https://plus.google.com/101584889282878921052/posts/3KfcsUy994b

My dog Luna, through Glass
https://plus.google.com/101584889282878921052/posts/axiVS2b4jDj

My portrait by +Bearman Cartoons 
https://plus.google.com/101584889282878921052/posts/V34HkBjd5mD

How many ways can a tie be tied?
https://plus.google.com/101584889282878921052/posts/RQrjPGQ6nwm

Wine glass photography (reshared from +Tiffany Lykins)
https://plus.google.com/101584889282878921052/posts/bATjvaZrcL4

Valentine's Day
https://plus.google.com/101584889282878921052/posts/1zHKQxAV4yn

The fractal music of Per Nørgård
https://plus.google.com/101584889282878921052/posts/RLuTaqtxc9j

Calvin Seibert's sandcastles
https://plus.google.com/101584889282878921052/posts/RuVoyCdhN4M

Herkimer Diamonds (reshared from +BJ Bolender)
https://plus.google.com/101584889282878921052/posts/9Z1KuS7sqd1

Automorphic numbers
https://plus.google.com/101584889282878921052/posts/JUPgnCtRvhx

Indra's pearls
https://plus.google.com/101584889282878921052/posts/eaaFWPKrNTr

Molecular machinery
https://plus.google.com/101584889282878921052/posts/cgBsTe3PbHd

As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!
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Engagers Showcase Circle, February 14, 2014

If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.

This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. Because it has been so long since the last edition of this circle, some of my recent posts have not been included here, but I will include them next time.

Everyone mentioned below is also included in the circle.

Beware of geeks bearing gifs
https://plus.google.com/101584889282878921052/posts/3jPVUtb4Fem

Stanley Park (reshared from +Alex Milton)
https://plus.google.com/101584889282878921052/posts/5PwJjn6qdhc

The Knight Sky (reshared from +Vincent Knight)
https://plus.google.com/101584889282878921052/posts/9jAvErWz3Zr

Cornwall painting (reshared from +Paul Haworth)
https://plus.google.com/101584889282878921052/posts/GaeDF8V3bTq

Prairie dogs
https://plus.google.com/101584889282878921052/posts/SUJSbQPdpA2

Glass towers (reshared from +Graeme McRae)
https://plus.google.com/101584889282878921052/posts/VspBXwaF8d2

Crete coastline (reshared from +Ralph Reichert)
https://plus.google.com/101584889282878921052/posts/jFCqBYxcubA

My cat Comet
https://plus.google.com/101584889282878921052/posts/1ZmQ5qKP5nr

Dispensing batter
https://plus.google.com/101584889282878921052/posts/CYbtWVa2EDm

The Diophantine quintuple conjecture
https://plus.google.com/101584889282878921052/posts/FNDF7e8pW9X

Sculpture (reshared from +Henry Segerman)
https://plus.google.com/101584889282878921052/posts/ZcqzpV7QSTf

Lapis lazuli beads (reshared from +BJ Bolender)
https://plus.google.com/101584889282878921052/posts/bHRrwabUqZB

Monticello Dam
https://plus.google.com/101584889282878921052/posts/1zVLA3GjGxY

My dog Rex
https://plus.google.com/101584889282878921052/posts/gWwdxuTbyTx

Mystery tree on my driveway
https://plus.google.com/101584889282878921052/posts/KGDKdshnii3

What would it be like on a toroidal planet?
https://plus.google.com/101584889282878921052/posts/3g1HbzqGNok

As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!
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♡ ♡ ♡ Happy Valentines Day ♡ ♡ ♡

You may not love math, but math loves you.

Here are some red heart-shaped cardioids rolling along a blue cycloid - drawn by Greg Egan, who probably never expected me to deploy this image in such a kitschy way. 

A cycloid is formed by rolling a circle along a line and tracing the motion of a point on that circle.  You can see a bunch of circles doing that here.  If their diameter is 1, the distance between neighboring circles is π. 

A cardioid is formed by rolling a circle on another circle of the same size, and tracing the motion of a point on the rolling circle.

Look carefully!    Each circle on top is rolling on the circle on bottom, and the marked point is tracing out a cardioid.  The tricky part is that the circle on bottom is also rolling, so the cardioid moves

And by how things are set up, the cardioid automatically rolls along the cycloid!

You can see a lot more pictures like this here:

http://johncarlosbaez.wordpress.com/2013/12/03/rolling-hypocycloids/

especially in the comments!
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Must have app for all love birds!
Introduction
"No facebook, no Google+, just privacy - iThinkOfYou is the premium social network for two..." 

iPhone / iPod / iPad App: http://goo.gl/FXr1Y

++ Number 2 of the best-selling Social Networking Apps in Germany ++ 

Wherever you are and whatever you’re doing – iThinkOfYou is the easiest way to send your partner a token of love and affection. Just touch the on-screen heart to remind that special someone that your heart beats for them. 

- No registration required 
- Completely private, secure and anonymous 
- Free chat service (faster than a speeding SMS) 
- Push notifications 
- 255 chars per text messages 
- Map and location service 
- Speed dialing, e-mail, SMS 
- Lots of lovely heartbeat animations 
- Emoji (Emoticon) support 
- 42 built-in Emoticons (Emoji) :-) :( (B) <3 :o 
- Statistic for heartbeats, chat and distances 

Every method of contacting your partner in a single app! 
Send messages with a heartbeat animation through our free chat service that can replace most, or even all, SMS messages between you and your loved one. If a chat message is not enough the QuickDial screen lets you make a call, send an SMS or compose an e-mail at the touch of a button. 

Look back on past heartbeats and messages! Look at the map and view from where in the world you’ve already got a heart from your partner. 
Below the heart you can see when you last received a heartbeat and can access a history of all heartbeats and messages. 
No Internet or network is not a problem: The app will remember any messages you want to send and forward them as soon as your connection is active. 

Special animations for many occasions! "Thinking of you", “Have a nice day” and "Dinner for two" are included for free and even more are available from the in-app store: “Good morning, “Good night”, "I am sorry", “I miss you”, “Merry Christmas”, "Happy Valentine's Day", ...

There is no registration or disclosure of personal information required to use iThinkOfYou. We do not collect and do not store any personal data. All messages are completely anonymous and are automatically deleted from our server as soon as they have been delivered to the recipient. Guarding your privacy is not just a promise, it’s an integral part of our technology! 

Also works with iPad and iPod Touch! Full Retina support! 

Please note, that your partner needs to install iThinkOfYou too. The best is to give the App as a present to your partner...
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