prompter: If 3 corners of a triangle are equidistant, what are the angles of the triangle?

assistant: Every triangle can have a center point such that all corners are equidistant to it. This is called the circumcenter of the triangle. In case you were wondering about the equilateral triangle, which has sides of equal length, these have 60° angles on all sides.

prompter: How do I do the Pythagoras formula?

assistant: The Pythagorean theorem is written like: a² + b² = c²
It is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c.

assistant: The Pythagorean theorem states that in a right triangle (a triangle with one angle measuring 90 degrees), the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, which is the hypotenuse.

To use the Pythagorean formula, follow these steps:

1. Identify which side is the hypotenuse (the longest side) and which are the two shorter sides.

2. Square the length of each of the two shorter sides.

3. Add the two squares from step 2.

4. Take the square root of the sum from step 3 to find the length of the hypotenuse.

In equation form, this can be expressed as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the two shorter sides.


To solve for the length of the hypotenuse, you would take the square root of both sides of the equation:

c = √(a^2 + b^2)

So, for example, if you have a right triangle with sides of length 3 and 4, you would plug these values into the formula:

c = √(3^2 + 4^2)
c = √(9 + 16)
c = √25
c = 5

Therefore, the length of the hypotenuse in this triangle is 5 units.

assistant: pythagorean theorem states that A² + B² = C² -- C being the length hypotenuse of the triangle, and A and B being the lengths of the other 2 sides. It holds true for any right triangle.

assistant: Each corner in an equidistant triangle is 60 degrees
60+60+60 = 180

prompter: 666 is the number of Satan, no wonder the Satanists love triangles. Do you think there might be a connection?

assistant: There is no evidence to suggest a connection between the angles of an equilateral triangle and the number 666 commonly associated with Satan. The idea of a connection between the two is likely based on mere coincidence or speculation.

It's important to remember that numbers and geometry are neutral, and any associations with them are typically based on cultural or historical contexts, rather than any inherent properties of the numbers or shapes themselves. So while some people might associate triangles or certain numbers with Satan or other entities, these associations are not based in fact and do not have any inherent significance.

assistant: There is a possibility but it is more likely that Satanists love triangles due to more symbolic reasons and because of historical precedent when Satanists were first established.

assistant: The angles of the triangle would be 90 degrees. The triangle would therefore be a special kind of triangle known as an equilateral triangle. This means that all three sides of the triangle are precisely the same length, and that all three angles are exactly 90 degrees.

prompter: Good to know. What does the symbol of a triangle with an eye in the middle mean?