k → ∞ Holiday Math
Score: 0 /8
by k → ∞ Studios — Master Temperature Conversions & Affine Relations

❄️ Welcome to Holiday Math! 🌴

From Cold to Warm...

Imagine yourself in Anchorage, Alaska in January. It's freezing! But you dream of sunny Montego Bay, Jamaica. To prepare for your tropical vacation, you need to master temperature conversions!

60s — Press Enter to skip

🌡️ Temperature Scales 🌡️

Four Temperature Scales

You'll convert between Celsius (°C), Fahrenheit (°F), Kelvin (K), and Rankine (°R). Each scale tells the same story of heat — just in different languages! Master them all to reach paradise!

Key Conversion Formulas

°F = (°C × 9/5) + 32 or (°C × 1.8) + 32
°C = (°F - 32) × 5/9 or (°F - 32) / 1.8
K = °C + 273.15
°C = K - 273.15
°R = °F + 459.67
°F = °R - 459.67
°R = K × 9/5
K = °R × 5/9
60s — Press Enter to skip

📚 How to Play

🎯
Your Mission: Answer 8 temperature conversion questions correctly to reach Montego Bay!
⏱️
Time Limit: You have 30 seconds for each question. Answer quickly and accurately!
📐
Conversions: You'll convert between Kelvin, Rankine, Celsius, and Fahrenheit in various combinations.
✈️
Travel Path: Each correct answer moves you closer to the tropics. Wrong answers keep you in the cold!
🏖️
Final Score: Get all 8 right to reach sunny Montego Bay. Otherwise, you'll end up somewhere in between!
💡
Pro Tip: Remember the formulas! They're all linear (affine) transformations of the form y = mx + b.
60s — Press Enter to skip

🌡️ Temperature Scale Background

Background 1: Celsius and Fahrenheit

The Celsius temperature scale is defined as a linear scale such that water freezes at 0 degrees and boils at 100 degrees (both at sea level). Similarly, the Fahrenheit temperature scale is defined linearly such that water freezes at 32 degrees and boils at 212 degrees (both at sea level).

Notice it takes 180 degrees Fahrenheit to go from the freezing point to the boiling point compared to only 100 for Celsius and the freezing point is already at 32 suggesting a conversion formula of: F = 180/100 C + 32 or simply

(1) F = 9/5 C + 32.

If we solve for C by first subtracting 32 from both sides and multiplying by 5/9, we find

(2) C = 5/9(F - 32)

converts Fahrenheit to Celsius. As we will later learn (1) is a slope intercept representation of a line while (2) is a point slope representation.

Background 2: Absolute Zero and Kelvin/Rankine

Absolute zero is the lowest possible temperature, where particles have the minimum possible energy and atomic motion (vibrations) essentially stops. This is very important to scientists and happens at C = -273.15 degrees Celsius or equivalently F = (C × 9/5) + 32 = (-273.15 × 9/5) + 32 = -459.67.

Rather than continuously deal with large negative numbers scientists have recentered the Celsius and Fahrenheit scales, called the Kelvin (K) and Rankine (R) scales, respectively by setting K = C + 273.15 and R = F + 459.67. The scaling ratio from Celsius to Fahrenheit remains the same so R = 9/5 K. Negative Kelvin or Rankine temperatures do not have physical meaning.

60s — Press Enter to skip

🎮 Ready for Your Vacation?

🎉 Your Journey Complete!

Final Score 0 /8

Montego Bay, Jamaica

28°C / 82°F

Congratulations! You've mastered temperature conversions and earned your tropical paradise vacation!

🌡️ Temperature Scale Background

Background 1: Celsius and Fahrenheit

The Celsius temperature scale is defined as a linear scale such that water freezes at 0 degrees and boils at 100 degrees (both at sea level). Similarly, the Fahrenheit temperature scale is defined linearly such that water freezes at 32 degrees and boils at 212 degrees (both at sea level).

Notice it takes 180 degrees Fahrenheit to go from the freezing point to the boiling point compared to only 100 for Celsius and the freezing point is already at 32 suggesting a conversion formula of: F = 180/100 C + 32 or simply

(1) F = 9/5 C + 32.

If we solve for C by first subtracting 32 from both sides and multiplying by 5/9, we find

(2) C = 5/9(F - 32)

converts Fahrenheit to Celsius. As we will later learn (1) is a slope intercept representation of a line while (2) is a point slope representation.

Background 2: Absolute Zero and Kelvin/Rankine

Absolute zero is the lowest possible temperature, where particles have the minimum possible energy and atomic motion (vibrations) essentially stops. This is very important to scientists and happens at C = -273.15 degrees Celsius or equivalently F = (C × 9/5) + 32 = (-273.15 × 9/5) + 32 = -459.67.

Rather than continuously deal with large negative numbers scientists have recentered the Celsius and Fahrenheit scales, called the Kelvin (K) and Rankine (R) scales, respectively by setting K = C + 273.15 and R = F + 459.67. The scaling ratio from Celsius to Fahrenheit remains the same so R = 9/5 K. Negative Kelvin or Rankine temperatures do not have physical meaning.