Schläfli symbol calculator
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Add, subtract, maybe handle a few functions if it’s advanced. To the stars, with Omni Star Shape Calculator!
Star shapes: pointy geometry
Star polygons are the shiniest shapes in geometry. Rather than relying on rigid, pre-programmed steps. And that’s okay
Symbolab’s AI Math Calculator is designed to meet students where they are and help them move forward.
Chooses a Structured Approach That Supports Understanding
Understanding the problem is just the beginning.
Admire the proportions of these quantities:
al=ba=cb=φ
Knowing this, we can almost understand why the pentagram got its reputation! But most calculators don’t tell you why the answer is right or where things went wrong.
A basic calculator does what it’s told. How many triangles are in a pentagram shape?
We counted...
Of the 196 country flags in the world, 40 of them contain stars. Do we need to mention the Star of David, a hexagram, or the shared symbolism associated with the pentagram from Hinduism to Neo-paganism?
You can also notice that the constructions of a star-shaped polygon create many triangles, the simplest bi-dimensional shape.
To make the game more entertaining, connect the outside points of the n-gram!
The pentagram is nothing but a five-pointed star shape. Here are the formulas for the side: don't worry if you see some 2 factors, blame trigonometry instead!
a=2⋅b⋅sin(135)c=b⋅2d=b+c
As for the heptagram, the fastest way to compute the area involves the separation of the octagram in an octagon with side a and eight triangles.
The designers of the national colors couldn't make up their minds!
Our favorite starred flag is the flag of Nepal: the only non-rectangular flag in the world also has a beautiful 12-pointed star which really makes it stand out!
Star-shaped polygons appear widely through sacred geometry. our star shape calculator will calculate all of the important elements of a star polygon in the blink of an eye!
Here you will learn everything about star-shaped polygons.
It’s slow, layered, sometimes stubborn, and it needs space to grow.
Why Choose Symbolab Over Other Math Calculators?
Plenty of calculators can compute an answer. It’s about building understanding, one step at a time.
Step-by-Step Solutions
This is where Symbolab’s AI Math Calculator stands out.
If a limit needs the chain rule, it explains why. Learn everything about this "magic" number at the golden ratio calculator!
Apart from those golden ratios, there are a couple more relationships holding in a five-pointed star shape:
a=b+cl=a+b
We can also calculate the value of the perimeter and the area.
For the perimeter, use the general formula above, substituting n=5. if was in e.g. Learn more with the star shape calculator at Omni Calculator!
We can calculate the geometric relationships for both shapes, but we warn you: we will use some trigonometry, and the formulas will start to look "ugly"!
a=2⋅b⋅sin(2180−(360/7))c=2⋅b⋅cos(7360)
The side of the boundary 7/3 comes from the formula:
d=2×cos(180−2×7360)l−l
The formula for the area requires we compute:
- The area of a heptagram with a side equal to a; and
- Seven times the area of an isosceles triangle with side d and base a.
A=(27⋅2a⋅d2−(2a)2)+(47⋅a2⋅cot(7π))
To conclude, the last "manageable" star-shaped polygon is the octagram, an eight-pointed star shape with an intriguing figure, rich in angles of 45°.
For the area, a specific formula is needed:
A=25⋅(5−25)⋅a2
More than pentagram: different star shapes
Let's check out different star shapes!
If we start from the hexagon (the bestagon), we can build the hexagram.
By definition, they are:
- Non-convex;
- Self-intersecting;
- Equilateral; and
- Equiangular polygons.
Let's look at all of these features one by one!
- Non-convex means that you can draw a line between two points inside the star-shaped polygon that passes outside its perimeter.
- Self-intersecting means that you can build all the different star shapes starting from a regular polygon and prolonging its vertexes until the extensions cross each other.
- Equilateral signifies that all the outer sides of the star-shaped polygon have the same length (latus is the Latin for side).
- Equiangular means that all the angles lying in the same "region" are equal.
The last two attributes of the star polygons automatically qualify them as regular polygons.
It supports topics such as algebra, calculus, trigonometry, and more.
If a problem looks confusing, Symbolab’s AI Math Solver is built to slow down the explanation.