Calculus is a branch of advanced mathematics that studies the differentiation and integration of functions and their applications. The core is to use mathematical methods to analyze rates of change and accumulated quantities. It's based on the theory of limits and consists of two main parts: differential calculus and integral calculus.
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In simple terms, differentiation is using the change of a straight line to approximate the change of a curve; it's basically the linear part of a function's change.
An exterior angle is formed by one side of a polygon and the extension of another side. The sum of the exterior angles of a polygon is always 360°.
"'Image' refers to a concept in mathematics. It's basically like a picture or quadrant, so it's simply called 'image'."
Graphical equations connect the solutions of algebraic equations with geometric shapes, using visual geometry to reflect the abstract ideas of algebra. The core idea is 'combining numbers and shapes'.
A convex polygon is a polygon where all the interior angles are less than 180 degrees, with no 'indentations,' and any line connecting two vertices stays inside the shape.
It's a small cube used for playing games or deciding wins and losses, with each side showing 1, 2, 3, 4, 5, or 6 dots.
Probability is a branch of math that studies the patterns of random events, showing the chance of something happening with a number between 0 and 1.
Two lines a and b are cut by a third line c. The angles that are on the same side of the cutting line c and on the same side of the two lines a and b are called corresponding angles. When lines a and b are cut by a third line c, 'three lines and eight angles' appear, which include 4 pairs of corresponding angles, 2 pairs of alternate interior angles, and 2 pairs of same-side interior angles.
When two lines are cut by a third line, the two angles on the same side of the transversal and inside the two lines are called consecutive interior angles. When the two lines are parallel, consecutive interior angles are supplementary (they add up to 180°). Conversely, if consecutive interior angles are supplementary, then the two lines are parallel.