Why minus 40 degree is numerically same in both Fahrenheit and Celsius I proved it graphically but still I want to know with curiosity why they are equal numerically? 🤔

You're absolutely right about -40° being the only temperature numerically equal on both the Celsius (°C) and Fahrenheit (°F) scales. While you can prove it graphically, there's also a specific reason behind this unique point of intersection.

Here's the explanation:

**1. Defining the Scales:**

As mentioned earlier, the Celsius and Fahrenheit scales use different reference points for freezing and boiling points of water:

* **Celsius:** 0°C for freezing and 100°C for boiling.

* **Fahrenheit:** 32°F for freezing and 212°F for boiling.

**2. Understanding the Conversion Formula:**

The conversion formula between Celsius and Fahrenheit is:

```

°C = (5/9) * (°F - 32)

°F = (9/5) * °C + 32

```

**3. Finding the Intersection Point:**

We're looking for the temperature where °C and °F become equal, so we can set them equal to each other:

```

°C = °F

```

Substituting the conversion formulas for each scale, we get:

```

(5/9) * (°F - 32) = (9/5) * °C + 32

```

**4. Solving for the Intersection:**

This equation becomes:

```

5°F - 160 = 9°C + 32

```

Combining like terms:

```

5°F = 9°C + 192

```

Now, we need to find the value for °C and °F that makes this equation true. We can see that if we subtract 192 from both sides:

```

5°F - 192 = 9°C + 192 - 192

```

This simplifies to:

```

5°F - 192 = 9°C

```

Looking closely, we notice that the coefficient of °C is 9, and on the other side, the difference between 192 and 160 is also 32. This is no coincidence!

**5. The Intersection Point Revealed:**

If we divide both sides by 9, we get:

```

(5/9) * (°F - 192) = °C

```

Substituting back the value of (5/9) from the initial conversion formula:

```

°C = °F - 192

```

Now, to make this equation true, we need to find a value for °F that is exactly 192 more than its corresponding °C value.

**The key point to understand is that the conversion formula itself creates this unique intersection point.** The specific ratio of 5:9 in the conversion formula, combined with the reference point differences (32°F and 0°C), results in this specific temperature (-40°) where both scales have the same numerical value.

Therefore, -40° is not a special temperature with inherent equivalence in both scales; it's a result of the chosen reference points and the specific conversion formula used. 

I hope this explanation satisfies your curiosity and goes beyond the graphical proof to offer a deeper understanding of the reasoning behind this unique point of intersection.