remotes::install_github("gabammour/heron")
library(heron)Heronâs library
Heronâs formula is a formula for finding the area of a triangle when you know the lengths of its three sides. It is named after the ancient Greek mathematician, Hero of Alexandria, who first described it.
\[A = \sqrt{s(s-a)(s-b)(s-c)}\]
where \(a\), \(b\), and \(c\) are the lengths of the sides of the triangle, \(s\) is the semiperimeter of the triangle, which is defined as \(s = \frac{1}{2}(a + b + c)\), and \(A\) is the area of the triangle. The reason Heronâs formula works is that it is based on the concept of the âHeronian triangle,âwhich is a triangle with integer sides and integer area. Heronâs formula gives the exact area of a Heronian triangle, and it turns out that every triangle can be split into two Heronian triangles. So, by using Heronâs formula to find the area of each of these two triangles and adding the results, you get the area of the original triangle.
How can I install it ?
The package must be install through my personal GitHub account. Install the library remotes and then :
For more information on this package, use :
?heronSierpiĆski triangle
The SierpiĆski triangle is a fractal that is formed through an iterative process known as the chaos game. Starting with a single equilateral triangle, each subsequent iteration involves selecting a random vertex of the triangle and placing a new triangle with sides that are half the length of the original triangle. The new triangle is positioned such that its base coincides with the side opposite the selected vertex of the previous triangle.
First iteration
[1] "The triangle area is 0.19"Second iteration
[1] "The triangle area is 0.14"Third iteration
[1] "The triangle area is 0.11"Fourth iteration
[1] "The triangle area is 0.0791"