The plate

Picture a round plate, twenty-four centimetres across. One common way to picture a balanced meal is to cut the plate into three parts. This is only a picture to think with, not a diet. If you need special food, ask a doctor.

A round plate $24$ cm across, cut in three. Just a picture, not a diet; for special food, ask a doctor.

Plate $24$ cm, three parts (a picture, not a diet).

Half the plate is vegetables and fruit. A quarter is grains, such as rice or bread. The last quarter is protein, such as beans, eggs or fish. A half, a quarter and a quarter make one whole plate.

Vegetables and fruit $\frac{1}{2}$, grains $\frac{1}{4}$, protein $\frac{1}{4}$, and $\frac{1}{2}+\frac{1}{4}+\frac{1}{4}=1$.

$\frac{1}{2}+\frac{1}{4}+\frac{1}{4}=1$.

As angles, the vegetable half is a hundred and eighty degrees, and each quarter is ninety degrees.

Angles: $180^{\circ }$ for vegetables and fruit, $90^{\circ }$ for each quarter, and $180+90+90=360$.

$180^{\circ }+90^{\circ }+90^{\circ }=360^{\circ }$.

Now a surprise about the size of the plate. Take a smaller plate, eighteen centimetres across. It is three quarters as wide, but it has only nine sixteenths of the space for food: a little more than half. A plate that is a bit narrower makes a big difference.

Radius $12$: area $\pi \times 12^2\approx 452$ cm${}^2$. The $18$ cm plate: $\pi \times 9^2\approx 254$ cm${}^2$. Ratio ${\left(\frac{3}{4}\right)}^2=\frac{9}{16}$, a little over half.

Plate $18$ instead of $24$: area $\pi r^2$, $\pi \times 9^2\approx 254$ against $\pi \times 12^2\approx 452$, ratio ${\left(\frac{3}{4}\right)}^2=\frac{9}{16}$.