Dr. Geo, be a geometer! - Tag - PharoBe a geometer2017-07-19T07:56:27+02:00Hilaire Fernandesurn:md5:38626DotclearMathematics seriesurn:md5:0c657851046cdd9a5dabf39c7020c2c92017-01-03T14:41:00+01:00OFSETMathematicsPharoprogrammingSmalltalk<p>My son came to me with a mathematics series, he need to find its
convergence. After the mathematics work is done, we want to confirm by calculus
the found limit. Dr. Geo can be of some help here.</p> <p>The series is S = Sum 1 / (k * (k + 1) * (k + 2)). Once cut in three parts
it is established it converges toward 1/4.</p>
<p>Then we fired up Dr. Geo to compute a few ten of thousand terms and its
sum.</p>
<p>In a Workspace we wrote this tiny script:</p>
<pre>
| u s |
u := [ :k| 1 / (k * (k + 1) * (k + 2) ) ].
s := 0.
1 to: 100000 do: [ :k | s := s + (u value: k) ].
Transcript show: s; tab; show: s asFloat; cr
</pre>
<p>...and we got the confirmation of our finding:</p>
<pre>
(1250037500/5000150001) 0.2499999999500015
</pre>
<p>What is interesting is the exact result Pharo gave us as a fraction number.
That's why we also asked for a float version of the sum to more easily realize
how close we were to 1/4.</p>Tiny, yet so beautifulurn:md5:3ba3c7569882c12d16d96c5a23cbd2382016-03-12T08:36:00+01:00OFSETPharoprogrammingSmalltalk<p><q> How do you introduce an unknown, alternative programming language
to other developers ? One way to do so is by showing lots of small examples.
That is what we did in Elegant Pharo Code — Beautiful & Powerful
One-liners, Expressions and Snippets.</q></p>
<p><img src="https://cdn-images-1.medium.com/max/2000/1*TH1xuJ2_657OHbA8EvIPQw.jpeg" alt="" height="114" width="172" /></p> <p>Sven Van Caekenberghe wrote a very nice article exposing the strong features
of Pharo. How this programming language and environment let you solve problem
very elegantly.</p>
<p>Pharo is the environment used for Dr. Geo</p>
<p><a href="https://medium.com/concerning-pharo/tiny-yet-so-beautiful-1ef5149c910e#.52mnr8nyq">
Read Sven's article</a></p>