Mathematics PDF

1. Arithmetic Sequence - A sequence with a constant difference between terms (e.g., 5, 10, 15, 20...). 2. Geometric Sequence - A sequence where each term is found by multiplying the previous term by a fixed number (e.g., 2, 4, 8, 16...). 3. Fibonacci Sequence - A sequence where each number is the su...

1. Arithmetic Sequence - A sequence with a constant difference between terms (e.g., 5, 10, 15, 20...). 2. Geometric Sequence - A sequence where each term is found by multiplying the previous term by a fixed number (e.g., 2, 4, 8, 16...). 3. Fibonacci Sequence - A sequence where each number is the sum of the two preceding ones (e.g., 1, 1, 2, 3, 5...). 4. Golden Ratio - An irrational number approximately equal to 1.618, seen in natural patterns. 5. Fractal - A pattern that exhibits self-similarity, where each part is a smaller copy of the whole. — 6. Symmetry - A property where an object is invariant under transformations like reflection or rotation. 7. Tessellation - A pattern made of shapes that fit together without gaps or overlaps (e.g., honeycomb). 8. Triangular Numbers - Numbers that can form an equilateral triangle when arranged as dots (e.g., 1, 3, 6, 10...). 9. Harmonic Sequence - A sequence whose reciprocals form an arithmetic sequence. 10. Pascal's Triangle - A triangular array of binomial coefficients often used in combinatorics. 11. Exponential Growth - A pattern where quantities increase rapidly at a constant rate relative to their size (common in geometric sequences). 12. Isosceles Right Triangle - A triangle with two equal sides and a right angle. 13. Fractal Tree - A natural fractal pattern where smaller branches split off from larger branches in a self-similar fashion. 14. Self-Similarity - A property of fractals where smaller portions resemble the whole structure. 15. Geodesic Sphere - A spherical structure made of triangles, like those found in soap bubbles. 16. Minimizing Surface Tension - A principle seen in nature, like in the shape of water droplets or clouds. 17. Logarithmic Spiral - A spiral that gets wider as it turns, seen in phenomena like galaxies or seashells. 18. Euclidean Geometry - A system of geometry based on flat space, used to describe basic shapes like circles and squares. 19. Pythagoras - An ancient Greek mathematician who believed numbers were the essence of all things, often linked to early discoveries in mathematical patterns. 20. Exponential Decay - A process where quantities decrease rapidly at a constant rate, often described by geometric sequences (e.g., radioactive decay).