Sphere mapping

From formulasearchengine
Jump to navigation Jump to search
Blue circle 0 is tangent to circles 1, 2 and 3, as well as to preceding circles −1, −2 and −3.

In geometry, Coxeter's loxodromic sequence of tangent circles is an infinite sequence of circles arranged so that any four consecutive circles in the sequence are pairwise mutually tangent. This means that each circle in the sequence is tangent to the three circles that precede it and also to the three circles that follow it.

The radii of the circles in the sequence form a geometric progression with ratio

k=φ+φ2.89005,

where φ is the golden ratio. k and its reciprocal satisfy the equation

(1+x+x2+x3)2=2(1+x2+x4+x6),

and so any four consecutive circles in the sequence meet the conditions of Descartes' theorem.

The centres of the circles in the sequence lie on a logarithmic spiral. Viewed from the centre of the spiral, the angle between the centres of successive circles is

cos1(1φ)128.173.

The construction is named after geometer Donald Coxeter, who generalised the two-dimensional case to sequences of spheres and hyperspheres in higher dimensions.

See also

External links



  • I had like 17 domains hosted on single account, and never had any special troubles. If you are not happy with the service you will get your money back with in 45 days, that's guaranteed. But the Search Engine utility inside the Hostgator account furnished an instant score for my launched website. Fantastico is unable to install WordPress in a directory which already have any file i.e to install WordPress using Fantastico the destination directory must be empty and it should not have any previous installation files. When you share great information, others will take note. Once your hosting is purchased, you will need to setup your domain name to point to your hosting. Money Back: All accounts of Hostgator come with a 45 day money back guarantee. If you have any queries relating to where by and how to use Hostgator Discount Coupon, you can make contact with us at our site. If you are starting up a website or don't have too much website traffic coming your way, a shared plan is more than enough. Condition you want to take advantage of the worldwide web you prerequisite a HostGator web page, -1 of the most trusted and unfailing web suppliers on the world wide web today. Since, single server is shared by 700 to 800 websites, you cannot expect much speed.



    Hostgator tutorials on how to install Wordpress need not be complicated, especially when you will be dealing with a web hosting service that is friendly for novice webmasters and a blogging platform that is as intuitive as riding a bike. After that you can get Hostgator to host your domain and use the wordpress to do the blogging. Once you start site flipping, trust me you will not be able to stop. I cut my webmaster teeth on Control Panel many years ago, but since had left for other hosting companies with more commercial (cough, cough) interfaces. If you don't like it, you can chalk it up to experience and go on. First, find a good starter template design. When I signed up, I did a search for current "HostGator codes" on the web, which enabled me to receive a one-word entry for a discount. Your posts, comments, and pictures will all be imported into your new WordPress blog.
  • H. S. M. Coxeter - The Descartes circle theorem and Fibonacci numbers