We have 36 small squares with a side length of 1 cm. The task is to spell out a rectangle or square with these small squares. We need to find out all possible splicing methods. Suppose the length of a rectangle is a cm and the width is b cm.

According to the topic, we can establish the following equation: the area of a rectangle is AXB = 36 cm 2 (length times width). Both a and b are positive integers, because the area cannot be a decimal or a fraction.

Now we need to find all the values of A and B that satisfy these conditions. The values of A and B that meet the requirements are as follows: Therefore, the dimensions of a rectangle or square consisting of 36 small squares with a side length of 1 cm are: length: 36 cm, width: 1 cm, length: 36 cm and width: 1 cm.

Knowledge expansion: how to cultivate mathematical three-dimensional sense

I. Introduction

Mathematics, a seemingly boring subject, actually hides endless mysteries and beauty. Stereo impression is an important concept in mathematics, especially in geometry. So, how to cultivate the three-dimensional sense of mathematics? This paper will discuss this issue to help readers better understand and master this concept.

Second, the meaning of three-dimensional sense

Stereoscopic sense, as its name implies, is the ability to recognize and perceive three-dimensional space. In mathematics, the three-dimensional sense is mainly reflected in the imagination, analysis and understanding of spatial graphics. Having a good three-dimensional sense can not only help us better understand complex geometric problems, but also stimulate our innovative spirit in the field of mathematics.

Third, the method of cultivating mathematical three-dimensional sense

1. Physical observation: By observing physical objects in life, such as spheres and cubes, we can intuitively feel three-dimensional shapes, thus enhancing our understanding of space.

2. Hands-on production: By making simple geometric models, you can experience the characteristics of three-dimensional shapes and deepen your understanding of spatial graphics.

3. Imagination training: Close your eyes, draw various three-dimensional figures in your mind, and transform them, such as rotation and translation. This kind of imagination training helps to improve our spatial imagination.

4. Learning theoretical knowledge: Understanding the basic concepts and theorems in geometry such as parallel lines, vertical lines and angles can help us better understand the essence of spatial forms.