Imaginary Numbers
Simplify: i10
-1
cos90o
0
d/dx( 3x2 + 2x - 1)
6x + 2
Area of a triangle with base 10 and height 9
45
He and his students constructed the proof, so this person gets credit for this famous theorem, even though it had been used previously by Babylonians and Indians. This mathematician believed that numbers had personalities like perfect or incomplete, masculine or feminine, beautiful or ugly.
Pythagoras
Simplify: sqrt(-20)
(2sqrt5)i
sin270o + tan225o
0
The slope of the line tangent to y= 3x2 + 2x - 1 at x = 2
14
Area of a semi-circle whose radius is 8
32π
The father of geometry
Euclid
Simplify: (3 - 2i)(3 + 2i)
13
Solve over [0, 2π): tan2x - 3=0
x = π/3, 2π/3, 4π3, 5π/3
y' = cosx + ex
Area of a trapezoid with bases 6 and 10, with a height of 7.
56
His work on ‘binomial coefficients’ guided Newton to discover the binomial theorem.
Pascal
Simplify: (5 + 4i)2
9 + 40i
Evaluate f(π/3), given f(x) = 4sin(x - π/6) + 1
Differentiate: (5x - 3)2
10(5x - 3) or 50x - 30
Given a circle with diameter 6, find the area of the sector formed by a 120o angle.
3π
He introduced many notations and symbols, including Σ, e for the natural log base, a, b and c for the sides of a triangle and A, B, and C for the opposite angles, f(x), i for √−1, and he popularized the use of the symbol π. His identity (eiπ + 1 = 0) is called, "the most beautiful equation".
Euler
Solve over the complex numbers: (x - 7)2 = - 100
x = 7 +/- 10i
Solve over [0o, 360o): cscx = secx
x = 45o, 225o
Differentiate: 2x.sinx
2.sinx + 2x.cosx or 2(sinx + xcosx)
The area of the region between the line y = (1/2)x - 3, the x-axis, and the line x = 10.
4
These TWO mathematicians independently invented and described calculus in Europe in the 17th century.
Leibniz and Newton