1. Earth’s axial tilt.

23.5°: Earth’s axial tilt—this is what causes the seasons.

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2. Descending order number.

“One” is the only number spelled with letters in descending alphabetical order

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3.

Leyland Numbers.

Leyland numbers are numbers of the form:

$x^y + y^x$

where $x > 1$ and $y > 1$ are integers.

Examples

Using small values of $x$ and $y$ :

$x$	$y$	Calculation	Leyland number
2	2	$2^2 + 2^2$	8
2	3	$2^3 + 3^2$	17
3	2	$3^2 + 2^3$	17
2	4	$2^4 + 4^2$	32
3	3	$3^3 + 3^3$	54
2	5	$2^5 + 5^2$	57

First few distinct Leyland numbers

$…8,\ 17,\ 32,\ 54,\ 57,\ 100,\ 145,\ 177,\ 320,\ 368,\ \dots$

Key properties

$x^y + y^x$ is symmetric, so swapping $x$ and $y$ gives the same number.
They grow very rapidly as $x$ and $y$ increase.
Some Leyland numbers are prime, for example:
- 17
- 100 (not prime, but notable as $4^2 + 2^4$ )
There are only a few known Leyland primes, and they are rare.

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4.

Fun Checking a Multiplication

A quick way to check if a long multiplication is correct.

Let’s check whether:

347×58=20,126

Step 1 — Reduce each number mod 9

347 → 3+4+7 = 14 → 1+4 = 5 58 → 5+8 = 13 → 1+3 = 4

Multiply the reduced forms: 5 × 4 = 20 → 2+0 = 2

Step 2 — Reduce the result mod 9

20,126 → 2+0+1+2+6 = 11 → 1+1 = 2

Step 3 — Compare

Left side = 2 Right side = 2

They match → the multiplication is very likely correct.

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5.

Babylonian Sexagesimal System:

Used base 60 for time and angles.

The Babylonian sexagesimal system was an ancient number system used by the Babylonians (Mesopotamia, around 2000 BCE) that is based on 60 (base-60) instead of 10 like we use today.

🧮 What “sexagesimal” means

“Sexagesimal” = base 60 system
Numbers are built using powers of 60 (like our base-10 uses powers of 10)

So instead of:

1, 10, 100, 1000 (base 10)

They used:

1, 60, 3600, 216,000 (base 60)

⏰ Why we still use it today

Even though the system itself is ancient, it survived in modern life:

🕒 Time

60 seconds = 1 minute
60 minutes = 1 hour

📐 Angles

360 degrees in a circle
1 degree = 60 minutes (arcminutes)
1 minute = 60 seconds (arcseconds)

🌍 Why 60?

The number 60 is useful because it has many divisors:

2, 3, 4, 5, 6, 10, 12, 15, 20, 30…

That makes fractions and measurements easier—especially for astronomy and trade.

🏛️ Historical significance

The Babylonians used this system for:

Astronomy (tracking planets and stars)
Mathematics and geometry
Calendars and timekeeping

It became one of the most influential number systems in history.

💡 Bottom line

Even today, every time you look at a clock or measure an angle, you’re still using a 3,000+ year-old Babylonian idea.

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Fun With Numbers

Leyland Numbers.

Examples

First few distinct Leyland numbers

Key properties

Fun Checking a Multiplication

Step 1 — Reduce each number mod 9

Step 2 — Reduce the result mod 9

Step 3 — Compare

Babylonian Sexagesimal System:

Used base 60 for time and angles.

🧮 What “sexagesimal” means

⏰ Why we still use it today

🕒 Time

📐 Angles

🌍 Why 60?

🏛️ Historical significance

💡 Bottom line

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