Mathematics 101
- Reminder of Fundamentals
- Advanced Arithmetics
- Introduction to Geometry
- In-depth Geometry
- Deeper into Numbers
- Further into Algebra
- Elementary Statistics & Probability
- Advanced Statistics, Probability
- Mathematical Logic
- Calculus
- Calculus
- Trigonometry I
- Trigonometry II & Conclusion
In-depth Geometry
Understanding Polygons and Circles
Branch of mathematics regarding geometric figures and properties of space.
Geometry, a branch of mathematics that deals with shapes and their properties, is a fundamental aspect of our world. In this unit, we will delve into two key geometric figures: polygons and circles.
Polygons
A polygon is a closed figure with three or more straight sides. Polygons come in many shapes and sizes, and understanding their properties can help us make sense of the world around us.
Types of Polygons
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Triangles: A polygon with three sides. Depending on the lengths of its sides, a triangle can be classified as equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal).
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Quadrilaterals: A polygon with four sides. Examples include squares, rectangles, parallelograms, and trapezoids.
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Pentagons: A polygon with five sides. A regular pentagon has all sides and angles equal.
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Hexagons: A polygon with six sides. A regular hexagon has all sides and angles equal.
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Heptagons: A polygon with seven sides. A regular heptagon has all sides and angles equal.
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Octagons: A polygon with eight sides. A regular octagon has all sides and angles equal.
And so on. The names continue based on Greek numerical prefixes.
Properties of Polygons
Each polygon has specific properties related to its sides, angles, and diagonals. For example, the sum of the interior angles of a polygon can be calculated using the formula (n-2) x 180°, where n is the number of sides.
Circles
A circle is a shape with all points the same distance from its center. It's a special type of ellipse and is of significant importance in geometry.
Key Parts of a Circle
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Radius: The distance from the center of the circle to any point on the circle.
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Diameter: The distance across the circle through the center. It is twice the radius.
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Circumference: The distance around the circle. It can be calculated using the formula 2πr, where r is the radius.
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Area: The number of square units that fit inside the circle. It can be calculated using the formula πr², where r is the radius.
Relationship Between Polygons and Circles
Polygons and circles are interconnected in many ways. For example, a circle can be inscribed in a polygon or a polygon can be inscribed in a circle. The more sides a polygon has, the more it approximates a circle.
By understanding polygons and circles, we can better understand the world around us. From the natural world to human-made structures, these shapes are everywhere. As we move forward in this course, we will continue to explore the fascinating world of geometry.