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it was super easy , lets see ahead, . more power to you
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AOA,
In this 15-minute lecture, all the previous concepts are covered in a very good way.
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Type of Number Definition and Properties
Natural Numbers Positive integers, excluding zero: 1, 2, 3, ...
Whole Numbers Natural numbers and zero: 0, 1, 2, 3, ...
Integers Positive and negative whole numbers, including zero: ..., -3, -2, -1, 0, 1, 2, 3, ...
Rational Numbers Numbers are expressible as a ratio (fraction) of two integers: 1/2, -3/4, 7, 3/1, ...
Irrational Numbers Numbers that cannot be expressed as a simple fraction: √2, π, e, ...
Real Numbers All numbers on the real number line, including rationals and irrationals.
Imaginary Numbers Numbers of the form "bi," where "b" is a real number and "i" is the imaginary unit (i^2 = -1). Example: 3i
Complex Numbers Numbers of the form "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit. Example: 2 + 4i
Prime Numbers Natural numbers greater than 1 that have exactly two distinct positive divisors (1 and themselves). Examples: 2, 3, 5, 7, 11, ...
Composite Numbers Natural numbers greater than 1 that have more than two distinct positive divisors. Example: 4, 6, 9, 10, ...
Perfect Numbers Natural numbers that are equal to the sum of their proper divisors. Example: 28 (1 + 2 + 4 + 7 + 14 = 28)
Amicable Numbers Pairs of natural numbers where the sum of the proper divisors of each number equals the other. Example: (220, 284)
Palindromic Numbers Numbers that read the same forwards and backward. Example: 121, 1331, 7777
Fibonacci Numbers A sequence of numbers where each number is the sum of the two preceding ones. Example: 0, 1, 1, 2, 3, 5, 8, ...
Triangular Numbers Numbers that can be arranged in the shape of an equilateral triangle. Example: 1, 3, 6, 10, 15, ...
Mersenne Primes Prime numbers can be written in the form 2^n - 1, where "n" is also a prime number. Example: 3, 7, 31, ...
Fermat Primes Prime numbers that can be written in the form 2^(2^n) + 1. Examples: 3, 5, 17, 257, ...
Perfect Powers Numbers that can be expressed as an integer raised to a positive integer power. Example: 8 (2^3), 27 (3^3), ...
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Pie
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Value of pi is 3.14159
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The record for the most decimal places of pi calculated is held by Timothy Mullican, who calculated pi to 50 trillion (50,000,000,000,000) decimal places on January 29, 2020, using the Bellard's formula and y-cruncher software.
The value of pi (π) has been calculated and approximated by many mathematicians throughout history. Here are a few notable individuals who contributed to the calculation of pi:Archimedes (287-212 BC): Estimated the value of pi using method of inscribed and circumscribed polygons and showed that pi is between 3 1/7 (approximately 3.1429) and 3 10/71 (approximately 3.1408).A Chinese mathematician Liu Hui (c. 263-303 AD): Improved on Archimedes' method and calculated pi with a 96-sided polygon obtaining a value accurate to five decimal places.Another Chinese mathematician Zu Chongzhi (429-500 AD): Used a 12,288-sided polygon to calculate the value of pi with great accuracy, up to seven decimal places.A Persian mathematician and scholar Al-Khwarizmi (circa 780-850 AD): worked on the calculation of pi contributed to the understanding of trigonometry and algebraic methods for approximating pi.An Indian mathematician and astronomer Madhava of Sangamagrama (c. 1340-1425 AD): who developed an infinite series to calculate the value of pi, anticipating the concept of calculus. He and his school members found several methods to approximate pi with remarkable accuracy.A German-Dutch mathematician Ludolph van Ceulen (1540-1610): spent much of his life calculating the value of pi. He calculated pi to 35 decimal places, and these digits were inscribed on his tombstone.John Wallis (1616-1703): An English mathematician who contributed significantly to the understanding of pi. He introduced the symbol π for the first time and studied infinite product expansions for pi
The lectures in the math playlist are amazing. Everything is taught from the very basics.
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