Question 4

We will count the finger joints on one hand and then connect this to ancient counting systems.

Step 1 — Counting on one hand

Let's find the number of fingers we use. The thumb is used for counting, not for its joints. So, we use 4 fingers for their joints. Each of these fingers has 3 joints. We multiply the number of fingers by the number of joints.

$\text{Total joints} = \text{Number of fingers} \times \text{Joints per finger}$

$= 4 \times 3$

$\boxed{12 \text{ joints}}$

Step 2 — Relating to base-12 system

We found that we can count up to 12 using one hand. This method naturally leads to a base-12 system. Ancient people likely used this method. So, they developed a base-12 counting system.

Answer

(i) We can count up to 12 on one hand. (ii) This relates to the ancient base-12 counting systems because the method allows counting exactly 12 units, making it a natural foundation for a duodecimal (base-12) system.