1.3.1 Top new questions this week

1.3.1.1 How many triangles are there?

http://mathematica.stackexchange.com/questions/59350/how-many-triangles-are-there

 
Some time ago I found a puzzle and it stopped my work until I solved it. 
 
 
 
One of the possible solutions: 
 
Let us sum upright and upside down triangles whose top lies in the 
$i$-th row. 
$$ 
...
 

- asked by ybeltukov (22 votes), answered by george2079 (20 votes)

1.3.1.2 Composition à la Mondrian

http://mathematica.stackexchange.com/questions/59620/composition-a-la-mondrian

 
I would like to paint something like this 
 
 
 
or,even better, like this 
 
 
 
I have tried 
 
colors = 
{Red, Blue, Yellow, White, Black}; 
 
cells = 
ConstantImage[RandomChoice[colors], #] & /@ 
...
 

- asked by eldo (21 votes), answered by Simon Woods (11 votes)

1.3.1.3 Homotopy Visualization

http://mathematica.stackexchange.com/questions/59463/homotopy-visualization

 
I noticed that both the lower cased 'i' and the Apple logo  are 
topologically equivalent to  the disjoint union of two closed discs. 
 
 
 
I'd like to animate a homeomorphism from the left to the right,  ...
 

- asked by Tobi Lehman (18 votes), answered by Michael E2 (28 votes)

1.3.1.4 Finding all paths of certain length between vertices in path graph,non-simple ones too

http://mathematica.stackexchange.com/questions/59554/finding-all-paths-of-certain-length-between-vertices-in-path-graph-non-simple-o

 
First I will tell you what my ultimate goal is, because maybe there's 
another way of doing it other than what I am trying. 
 
I need a list of all $(a_1, a_2, \ldots, a_N)$ tuples that satisfy 
certain  ...
 

- asked by luke (12 votes), answered by ybeltukov (7 votes)

1.3.1.5 How to manipulate a circle in GeoGebra style?

http://mathematica.stackexchange.com/questions/59726/how-to-manipulate-a-circle-in-geogebra-style

 
I want to emulate the GeoGebra app. I want to get an effect like this in 
Mathematica. 
 
 
 
I don't know how to move whole circle without changing the radius of the 
circle. 
 
My sample code 
 
...
 

- asked by mathe (11 votes), answered by Kuba (5 votes)

1.3.1.6 Splitting strings into letter keys and integers

http://mathematica.stackexchange.com/questions/59690/splitting-strings-into-letter-keys-and-integers

 
I have strings of the following form: 
 
string = "ABC123DEFG456HI89UZXX1"; 
 
 
Letter keys of variable lengths are followed by (positive) integers. 
 
I want to get this transformation: 
 
 
{{"ABC", 123},  ...
 

- asked by eldo (11 votes), answered by RunnyKine (10 votes)

1.3.1.7 Mathematica isn't sure whether a sum of two positives is positive or not

http://mathematica.stackexchange.com/questions/59589/mathematica-isnt-sure-whether-a-sum-of-two-positives-is-positive-or-not

 
Mathematica is not able to tell whether a summation of two positive 
expressions is positive or not. Which is very strange. 
 
My three symbolic arguments, $x$, $y$, and $z$, are all real numbers 
bounded  ...
 

- asked by jim (10 votes), answered by Jens (9 votes)