Mathematical constants (pi, e, golden ratio) in SciPy - Mini Project: Build & Apply

Using Mathematical Constants with SciPy

📖 Scenario: You are working on a simple science project where you need to use important mathematical constants like pi, e, and the golden ratio. These constants help in many calculations in science and nature.

🎯 Goal: You will create a Python program that stores these constants using SciPy and then prints them out. This will help you understand how to use built-in constants in Python for your calculations.

📋 What You'll Learn

Use the scipy.constants module to access constants

Create variables for pi, e, and golden_ratio with exact values from SciPy

Print the values of these constants

💡 Why This Matters

🌍 Real World

Mathematical constants like pi and e are used in physics, engineering, and computer science to solve real problems involving circles, growth, and patterns.

💼 Career

Knowing how to use built-in constants helps data scientists and engineers write accurate and efficient code for scientific calculations.

1

Import SciPy constants and create variables

Write code to import scipy.constants as const. Then create three variables called pi, e, and golden_ratio and assign them the values const.pi, const.e, and const.golden_ratio respectively.

SciPy

# Import scipy.constants as const
# Create variables pi, e, and golden_ratio with values from const
# Your code here

Hint

Use import scipy.constants as const to import the constants module. Then assign pi = const.pi, e = const.e, and golden_ratio = const.golden_ratio.

2

Create a list of constants

Create a list called constants_list that contains the variables pi, e, and golden_ratio in that order.

SciPy

import scipy.constants as const

pi = const.pi
e = const.e
golden_ratio = const.golden_ratio

# Create a list called constants_list with pi, e, and golden_ratio
# Your code here

Hint

Use square brackets to create a list: constants_list = [pi, e, golden_ratio].

3

Create a dictionary with constant names and values

Create a dictionary called constants_dict with keys 'pi', 'e', and 'golden_ratio' and their corresponding values from the variables pi, e, and golden_ratio.

SciPy

import scipy.constants as const

pi = const.pi
e = const.e
golden_ratio = const.golden_ratio

constants_list = [pi, e, golden_ratio]

# Create a dictionary constants_dict with keys 'pi', 'e', 'golden_ratio' and their values
# Your code here

Hint

Create a dictionary with curly braces and key-value pairs like {'pi': pi, 'e': e, 'golden_ratio': golden_ratio}.

4

Print the constants dictionary

Write a print statement to display the constants_dict dictionary.

SciPy

import scipy.constants as const

pi = const.pi
e = const.e
golden_ratio = const.golden_ratio

constants_list = [pi, e, golden_ratio]

constants_dict = {'pi': pi, 'e': e, 'golden_ratio': golden_ratio}

# Print the constants_dict dictionary
# Your code here

Hint

Use print(constants_dict) to show the dictionary on the screen.

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