Mathematical constants (pi, e, golden ratio) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of pi constant from scipy

What is the output of this code snippet that prints the value of pi from scipy.constants?

SciPy

from scipy.constants import pi
print(round(pi, 4))

A 3.1416

B 3.14

C 3.142

D 3.1415

💡 Hint

Use round() to 4 decimal places on pi constant.

The scipy.constants.pi value is approximately 3.141592653589793. Rounded to 4 decimals, it becomes 3.1416.

❓ data_output

intermediate

Value of Euler's number (e) from numpy

What is the value of Euler's number (e) from numpy when rounded to 3 decimals?

SciPy

from numpy import e
print(round(e, 3))

A 2.719

B 2.718

C 2.717

D 3.142

💡 Hint

Euler's number e is about 2.71828.

The constant e from numpy is approximately 2.718281828459045. Rounded to 3 decimals, it is 2.718.

🧠 Conceptual

advanced

Understanding the golden ratio constant

Which of the following statements about the golden ratio constant from scipy.constants is true?

A It is the same as pi but used in geometry.

B It is exactly 1.5 and used mainly in computer science algorithms.

C It is a variable constant that changes with time.

D It is approximately 1.618 and represents a special ratio in nature and art.

💡 Hint

Think about the unique properties of the golden ratio.

The golden ratio is approximately 1.6180339887 and appears in nature, art, and architecture as a pleasing proportion.

❓ Predict Output

advanced

Calculate the sum of pi, e, and golden ratio constants

What is the output of this code that sums pi and golden from scipy.constants and e from numpy and rounds to 5 decimals?

SciPy

from scipy.constants import pi, golden
from numpy import e
result = pi + e + golden
print(round(result, 5))

A 7.47790

B 7.47793

C 7.47791

D 7.47792

💡 Hint

Add the three constants and round the sum to 5 decimals.

pi ≈ 3.141592653589793 (scipy.constants), e ≈ 2.718281828459045 (numpy), golden ≈ 1.618033988749895 (scipy.constants). Sum ≈ 7.477908470798733. Rounded to 5 decimals: 7.47791.

🔧 Debug

expert

Identify the error in accessing the golden ratio constant

What error will this code raise when trying to import and print the golden ratio constant from scipy.constants?

SciPy

from scipy.constants import golden_ratio
print(golden_ratio)

A ImportError

B ModuleNotFoundError

C AttributeError

D NameError

💡 Hint

Check the exact name of the golden ratio constant in scipy.constants.

The golden ratio constant in scipy.constants is named 'golden', not 'golden_ratio'. Trying to import 'golden_ratio' causes ImportError.

Practice

1. Which of the following constants is NOT directly available in scipy.constants?

easy

A. pi

B. e

C. golden ratio

D. Avogadro's number

Solution

1. Step 1: Recall scipy.constants common constants

   Scipy provides many constants like pi, e, and the golden ratio directly accessible.

2. Step 2: Check Avogadro's number availability

   Avogadro's number is not included in scipy.constants; it is usually found in other libraries like scipy.constants.physical_constants.

3. Final Answer:

   Avogadro's number -> Option D

4. Quick Check:

   Avogadro's number not in scipy.constants [OK]

Hint: Remember scipy.constants has math constants, not all physical constants [OK]

Common Mistakes:

• Assuming all physical constants are in scipy.constants
• Confusing golden ratio with Avogadro's number
• Thinking Avogadro's number is a math constant

2. Which is the correct way to import the constant pi from scipy?

easy

A. from scipy.constants import pi

B. import scipy.pi

C. from scipy import pi

D. import pi from scipy.constants

Solution

1. Step 1: Understand Python import syntax

   To import a specific item from a module, use from module import item.

2. Step 2: Apply correct import for pi

   Since pi is inside scipy.constants, the correct import is from scipy.constants import pi.

3. Final Answer:

   from scipy.constants import pi -> Option A

4. Quick Check:

   Correct import syntax for pi [OK]

Hint: Use 'from module import item' for constants [OK]

Common Mistakes:

• Using 'import scipy.pi' which is invalid
• Trying 'from scipy import pi' without constants
• Incorrect import order like 'import pi from ...'

3. What is the output of this code?

from scipy.constants import golden_ratio
print(round(golden_ratio, 3))

medium

A. 3.142

B. 1.618

C. 2.718

D. 1.414

Solution

1. Step 1: Identify the constant used

   The code imports golden_ratio from scipy.constants, which is approximately 1.6180339887.

2. Step 2: Apply rounding to 3 decimals

   Rounding 1.6180339887 to 3 decimals gives 1.618.

3. Final Answer:

   1.618 -> Option B

4. Quick Check:

   golden_ratio ≈ 1.618 [OK]

Hint: Golden ratio rounds to 1.618 [OK]

Common Mistakes:

• Confusing golden ratio with pi or e
• Rounding incorrectly to 3 decimals
• Printing without importing golden_ratio

4. Find the error in this code snippet:

from scipy.constants import e
print(e())

medium

A. e is a constant, not a function; remove parentheses

B. Import statement is incorrect

C. e needs to be converted to string before printing

D. Parentheses are required to call e

Solution

1. Step 1: Understand what e represents

   In scipy.constants, e is a constant value (Euler's number), not a function.

2. Step 2: Identify misuse of parentheses

   Calling e with parentheses e() tries to call a float as a function, causing an error.

3. Final Answer:

   e is a constant, not a function; remove parentheses -> Option A

4. Quick Check:

   Constants are values, not callable functions [OK]

Hint: Constants are values, don't add () [OK]

Common Mistakes:

• Trying to call constants as functions
• Incorrect import syntax
• Thinking constants need conversion before print

5. You want to calculate the area of a circle with radius 3 using scipy constants. Which code snippet correctly uses the constant pi for this calculation?

hard

A. import scipy.constants as sc
area = sc.pi(3) ** 2
print(area)

B. from scipy.constants import e
area = e * 3 ** 2
print(area)

C. from scipy.constants import pi
area = pi * 3 ** 2
print(area)

D. from scipy.constants import golden_ratio
area = golden_ratio * 3 ** 2
print(area)

Solution

1. Step 1: Identify the correct constant for circle area

   The area of a circle formula is pi times radius squared, so we need pi.

2. Step 2: Check code correctness

   from scipy.constants import pi area = pi * 3 ** 2 print(area) imports pi correctly and calculates area as pi * 3^2, which is correct.

3. Step 3: Verify other options

   import scipy.constants as sc area = sc.pi(3) ** 2 print(area) tries to call pi as a function, which is wrong. Options C and D use wrong constants (e and golden_ratio) for area.

4. Final Answer:

   from scipy.constants import pi area = pi * 3 ** 2 print(area) -> Option C

5. Quick Check:

   Use pi * r^2 for circle area [OK]

Hint: Use pi constant directly for circle area [OK]

Common Mistakes:

• Calling pi as a function
• Using wrong constants for area
• Incorrect import or calculation syntax