Discovered a neat formula (equilateral triangles)

[shadowboy13]

If you use this formula: $s^2$$\times$$\sqrt{3}$$\div4$ it gives you the area of said equilateral triangle.

I guess it's pretty neat i discovered it, but it doesn't seem very useful overall, anyone know any other uses for it?

 

[Mark44]

If you use this formula: $s^2$$\times$$\sqrt{3}$$\div4$ it gives you the area of said equilateral triangle.

I guess it's pretty neat i discovered it, but it doesn't seem very useful overall, anyone know any other uses for it?

Not to diminish your discovery in any way, but that formula has been known for a long time. For an equilateral triangle, all three interior angles are 60°. If you orient the triangle so that one of the sides is horizontal, the bisector of the angle at the top divides the base into two equal segments, and divides the triangle into two congruent 30° - 60° right triangles. The base of each of these smaller triangles is s/2. Using the theorem of Pythagoras or trig, one can find that the shared vertical side of the two triangles is s * $\sqrt{3}/2$. Having found this information, the area of the larger triangle is (1/2)*base*height = $(s/2) *s *\sqrt{3}/2$, same as what you discovered..

 

[jbunniii]

I'm not sure what other uses you envision aside from calculating the area of an equilateral triangle. You can use it as a building block to find the areas of objects that can decomposed into equilateral triangles, for example a regular hexagon with side $s$ can be broken into six equilateral triangles of side $s$, so its area is $3\sqrt{3}s^2/2$.

 

[Mentallic]

Let's not crush shadowboy's accomplishment all at once now.

I remember when my class was learning about Pythagoras' theorem, and soon later I figured out the distance from one corner of a cube to the opposite corner. I felt like I had stumbled onto something brilliant.

But of course, my teacher felt the need to slap some sense into me, and from that day on I never again felt like any of my personal discoveries were feats of genius.

It didn't stop me from searching for new neat little formulas though! Keep it up shadowboy13.

 

[CellCoree]

I can see the potential usefulness of this formula in various applications. Equilateral triangles are a fundamental shape in geometry and are commonly found in nature, architecture, and engineering. Being able to quickly and accurately calculate their area using this formula can save time and effort in designing and constructing structures or analyzing patterns in natural phenomena.

Furthermore, this formula can also be applied in fields such as computer graphics and animation, where equilateral triangles are often used as the basis for creating complex shapes and objects. The ability to easily calculate their area can greatly enhance the efficiency of these processes.

Overall, while this formula may seem simple, it has the potential to be a valuable tool in a wide range of scientific and practical applications. It's always exciting to discover new formulas and equations that can simplify and improve our understanding and manipulation of the world around us.