A solid has ashape, size, andposition, and can be moved from one place to another.
The interior angles of a triangle sum up to 180°
Parallel lines never cross each other
The shortest distance between two points is a straight line
Seven Euclidean Axioms
Things which are equal to the same thing are equal to one another.
If equals are added to equals, the wholes are equal.
If equals are subtracted from equals, the remainders are equal.
Things which coincide with one another are equal to one another.
The whole is greater than the part.
Things which are double of the same things are equal to one another.
Things which are halves of the same things are equal to one anothe
Euclid’s Five Postulates
A straight line segment may be drawn from any given point to any other.
A straight line may be extended to any finite length.
A circle may be described with any given point as its center and any distance as its radius.
All right angles are congruent.
Parallel Postulate: f a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles.
How does the Euclidean Geometry Calculator work?
Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid
What 6 concepts are covered in the Euclidean Geometry Calculator?
angle
the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
geometry
study of math dealing with shapes, space, and properties of space
line
an infinitely long one-dimensional object with no width, depth, or curvature
plane
a flat, two-dimensional surface that extends indefinitely
point
an exact location in the space, and has no length, width, or thickness
