Introduction to Delta Symbol
The fourth letter of the Greek alphabet refers to the delta. Delta symbol was derived from the Phoenician letter dalet 𐤃. Furthermore, the delta is a symbol that has significant usage in mathematics.
Delta symbol can represent a number, function, set, and equation in maths. Student can learn more about the delta symbol and its meaning in maths here.
Delta Symbol: Change
Uppercase delta (Δ) at most times means “change” or “the change” in maths. Consider an example, in which a variable x stands for the movement of an object. So, “Δx” means “the change in movement.” Scientists make use of this mathematical meaning of delta in various branches of science.
Delta Symbol: Discriminant
Uppercase delta (Δ) in algebra represents the discriminant of a polynomial equation. This polynomial equation is almost always the quadratic equation. Consider the quadratic ax2+bx=c, the discriminant of this equation would equal b2-4ac, and it would certainly look like this: Δ= b2-4ac.
A discriminant provided information regarding the quadratic roots. Most noteworthy, a quadratic may have two real roots, one real root, or two complex roots. Moreover, this depends on the value of Δ.
Delta Symbol: Geometry and Angles
In the field of geometry, lower-case delta (δ) may be representative of an angle in any geometric shape. This is primarily because geometry has its roots in Euclid’s work of ancient Greece. Consequently, mathematicians marked their angles with Greek letters.
The knowledge and understanding of the Greek alphabet are not necessary. This is because; the letters merely represent the angles.
Delta Symbol: Partial Derivatives
The derivative of a function refers to a measure of infinitesimal changes in one its variables. Furthermore, the roman letter “d” is representative of a derivative.
Partial derivatives differ from regular derivatives. This is because the function consists of multiple variations but there is the consideration of one variable. The other variables certainly stay fixed. Also, a lower-case delta (δ) indicates partial derivatives. Therefore, the partial derivative of function “f” looks like this: δf over δx.
Lowercase Delta(Kronecker Delta)
Lowercase delta (δ) have a much more specific function in maths of advance level. Furthermore, lowercase delta denotes a change in the value of a variable in calculus.
Consider the case for kronecker delta for example. Kronecker delta indicates a relationship between two integral variables. This is 1 if the two variables happen to be equal. Furthermore, this is 0 if the two variables are not equal.
Solved Question for You
Q1. Which of the following statements is not true with regards to the delta symbol in maths?
A. In trigonometry, lower-case delta (δ) represents the area of a triangle
B. Uppercase delta (Δ) at oftentimes means “change” or “the change” in maths.
C. Uppercase delta (Δ) in algebra represents the discriminant of a polynomial equation.
D. In geometry, lower-case delta (δ) may be representative of an angle in any geometric shape
A1. The correct answer is option A., Which is “In trigonometry, lower-case delta (δ) represents the area of a triangle.” This is because; lower-case delta (δ) does not represent the area of a triangle in trigonometry.