9. (ОБЗ) Размер (высота) типографского шрифта измеряется в пунктах. Один пункт равен 1/72 дюйма, то есть 0,3528 мм. Текст напечатан шрифтом высотой 20 пунктов на листе формата А2. Какой высоты нужен шрифт (в пунктах), чтобы текст был расположен на листе формата АЗ таким же образом? Размер шрифта округляется до целого.

The problem states that the text is printed on A2 paper with a font height of 20 points. We need to find the font height in points for A3 paper such that the text is arranged in the same way. The key is that the text should be arranged "in the same way", implying a similar density or scaling factor relative to the paper size. However, a more direct interpretation is that the *visual appearance* or *relative size* of the text to the paper should be consistent. Since A3 is larger than A2, and the text arrangement is to be the same, a larger font size might be needed if the text content is the same and is intended to occupy a proportionally similar area. However, the question is phrased such that the *text* is placed on A3, and we need to find the font size *in points* for that to happen "in the same way". This implies a proportional scaling. The ratio of A3 to A2 dimensions is \( \sqrt{2} \approx 1.414 \). If we assume the text should scale proportionally to the paper size to maintain the same "arrangement" (e.g., same number of lines fitting, same margins relative to size), we might scale the font size by this factor. So, \( 20 \text{ points} \times \sqrt{2} \approx 20 \times 1.414 \approx 28.28 \) points. Rounding to the nearest whole number gives 28 points.

Let's re-evaluate the interpretation of "arranged in the same way". If it means the same number of characters or words per line, and the same number of lines per page, then the text itself would need to scale proportionally with the paper. Since A3 is larger than A2, and assuming the same amount of text is being printed, the font size would need to increase to maintain the same visual density or spacing. A more common interpretation in typography related to paper sizes is that when moving to a larger paper size (like A3 from A2), if you want the same *visual impact* or *density of text*, you would increase the font size. The scaling factor between consecutive A-series paper sizes is \( \sqrt{2} \). Therefore, to maintain a similar layout or scaling, the font size should also scale by \( \sqrt{2} \).

20 points * \( \sqrt{2} \approx 20 * 1.4142 \approx 28.284 \)

Rounding to the nearest whole number, we get 28 points.

Пошаговое решение:

1. Размеры листов бумаги серии А соотносятся как \( \sqrt{2} \). Формат А3 больше формата А2, и отношение их размеров (например, длины) равно \( \sqrt{2} \).
2. Чтобы текст был расположен на листе формата А3 "таким же образом", как на листе формата А2, необходимо увеличить размер шрифта пропорционально увеличению формата бумаги.
3. Исходный размер шрифта на А2 = 20 пунктов.
4. Увеличиваем размер шрифта на коэффициент \( \sqrt{2} \): \( 20 \text{ пунктов} \times \sqrt{2} \approx 20 \times 1.4142 \approx 28.284 \text{ пункта} \).
5. Округляем до целого числа: 28 пунктов.

Ответ: 28