Mathematical constants (pi, e, golden ratio) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the constant pi from scipy.

SciPy

from scipy.constants import [1]
print(pi)

Drag options to blanks, or click blank then click option'

Agolden

Bpi

Ce

Dtau

Attempts:

3 left

💡 Hint

Common Mistakes

Importing 'e' instead of 'pi'.

Using 'golden' which is the golden ratio, not pi.

The constant pi is imported from scipy.constants to use the value of π.

2fill in blank

medium

Complete the code to print the value of the mathematical constant e from scipy.

SciPy

from scipy.constants import [1]
print(e)

Drag options to blanks, or click blank then click option'

Api

Bphi

Cgolden

De

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing 'pi' with 'e'.

Using 'golden' which is the golden ratio, not e.

The constant e is the base of natural logarithms and is imported from scipy.constants.

3fill in blank

hard

Fix the error in the code to correctly import and print the golden ratio constant from scipy.

SciPy

from scipy.constants import [1]
print(golden)

Drag options to blanks, or click blank then click option'

Agolden_ratio_value

Bphi

Cgolden

Dgolden_ratio

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'golden_ratio' which is not defined in scipy.constants.

Trying to import 'phi' which is not the correct name.

The golden ratio constant is named golden in scipy.constants. Using golden imports it correctly.

4fill in blank

hard

Fill both blanks to create a dictionary with keys 'pi' and 'e' and their values from scipy.constants.

SciPy

constants = {'pi': [1], 'e': [2]
print(constants)

Drag options to blanks, or click blank then click option'

Api

Be

C3.14

D2.71

Attempts:

3 left

💡 Hint

Common Mistakes

Using approximate float values instead of constants.

Mixing up keys and values.

Use the constants pi and e imported from scipy.constants to assign their exact values in the dictionary.

5fill in blank

hard

Fill all three blanks to create a dictionary with keys 'pi', 'e', and 'golden' and their values from scipy.constants.

SciPy

constants = {'pi': [1], 'e': [2], 'golden': [3]
print(constants)

Drag options to blanks, or click blank then click option'

Api

Be

Cgolden

Dphi

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'phi' instead of 'golden'.

Using approximate numbers instead of constants.

Use the constants pi, e, and golden from scipy.constants to fill the dictionary values correctly.

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