![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKhWE06qmuysFWfNDk-ClMNXKNFJctreGT6q4rFV-bUKI-SFwvUVFqQB4P3s-BuNulYvrDkpBL6IkgFt5pA7AT4C0zAec9g5lid0SlkTD9rXxp71vKRBoU_UAz6H4Hc6UOGFxXwfH8Ga8s/s1600/pi12a.jpg)
March 14, 2015, is the last day the U.S. date will align with the first five digits of pi (3,1415) until 2115.
photos by Styrous®
The circumference of a circle is slightly more than three times as long as its diameter.
The exact ratio is called π.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7rHzzXn62ztFb1LCy_YxDyRQayx7xOdR47KJnT-U0R_dUSfWNJccKxogHBMX6HlVDOBSXZo5NdCHiCq_4r-DjZASP_OsDBoiYryMVbHaghXtbt5TRJUzvDzYDdTfy7DQBTFcq6F9o75Zo/s280/1280px-Mandel_zoom_00_mandelbrot_set.jpg)
π can be computed from the Mandelbrot set, by counting the
number of iterations required before point (−0.75, ε) diverges.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibm5-eHMPi59ShRi6-AmMjh_KRz0scHcCEdZBOziiu7zC7Qz8I0zp9XcUQuBcvEsXUrxuzj9uA80cDcO0JXSly4442qJGVjIDaZtThWzW_jnb4TQ9-i9ZmReLBE1b5JSu5rzZdf71Gpd74/s280/220px-Squaring_the_circle.png)
Because π is a transcendental number, squaring the circle is not possible in a finite number of steps using the classical tools of compass and straightedge.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoA7k1-jl_uqSqGzY8BCCYIuklvVjEdBptkoJGeujTL2SelCtljBgacvel9AGBTSgF0CGplVjutgkWWJYy3x_dyBi42WDJljtersAJyuHp8tOLPZYVY8Wtbgy80p5-WOreXMoMvt6MjjiQ/s280/350px-Archimedes_pi.png)
π can be estimated by computing the perimeters of circumscribed and inscribed polygons. Check out the humorous article, Prehistoric Calculus: Discovering Pi, by Kalid Azad who makes use of these polygons to demonstrate π (link below).
A graph of the Gaussian function
ƒ(x) = e−x2. The colored region between the function and the x-axis has area
Random dots are placed on the quadrant of a square with a circle inscribed in it.
Styrous® ~ Saturday, March 14, 2015
No comments:
Post a Comment
PLEASE NOTE: comments are moderated BEFORE they are posted so DO NOT appear immediately.
Thank you.