History
What is Euler's full name
Leonhard Euler
What constant is represented by the letter e?
The base of natural logarithmic.
Evaluate e^0
1
What is Euler’s famous identity?
eiπ+1=0
What symbol did Euler popularize to represent summation?
Σ (sigma)
18th century
What is the approximate value of e to two decimal places?
2.718
Evaluate d/dx ex
ex
Which three constants appear in Euler’s identity?
e, π, and i
What letter did Euler popularize to represent a function’s input
x
Where is Leonhard Euler from?
Switzerland
What does e represent in exponential growth?
It is the base that models continuous growth or decay.
Solve for x: e2x−1=ex+3
4
What type of numbers does Euler’s formula connect (real, imaginary, complex)?
Which Greek letter did Euler introduce to represent angles in trigonometry?
theta or phi
Name one specific math field Euler contributed to.
Graph theory, number theory, complex analysis, or topology.
Why is e considered a “natural” number in mathematics?
It arises naturally from limits, continuous compounding, and calculus.
Use Euler’s formula to find the real part of eiπ
-1
State Euler’s formula.
eix= cos(x)+ isin(x)
What branch of mathematics did Euler effectively found with the Königsberg bridges problem?
Graph Theory
Which scientific academy did Euler work for most of his life?
St. Petersburg Academy of Sciences.
Explain why e appears in calculus when dealing with rates of change.
Because the derivative of exe^xex is itself.
Use Euler’s formula to rewrite eiπ/2 in the form a + bi
i
Explain why Euler’s identity is considered mathematically elegant.
It connects fundamental constants and multiple areas of mathematics in a single simple equation.
What is the name of the constant γ (gamma) that Euler studied in relation to harmonic series?
Euler–Mascheroni constant