2024年4月13日发(作者：)

压强切割和叠加问题解题思路

英文回答：

Understanding Pressure Cutting and Stacking Problems.

Pressure cutting and stacking problems are a form of

physics questions in which a series of cuts are made on a

sheet of material, and the remaining pieces are stacked

together to form a shape with a given set of dimensions.

These problems can be solved using a combination of logic

and geometry.

Key Concepts.

Pressure cutting: A cut in which a force is applied to

a material, causing it to break along a certain line.

Stacking: The process of arranging pieces of material

on top of each other to form a desired shape.

Perimeter: The total length of the boundary of a shape.

Area: The amount of space occupied by a shape.

Symmetry: A shape that has a mirror image or multiple

mirror images.

Problem Solving Steps.

1. Understand the given information. Read the problem

carefully and identify the following:

The shape and dimensions of the starting material.

The number and locations of the cuts.

The shape and dimensions of the desired end

product.

2. Determine the cuts that are necessary. Use the given

information to figure out which cuts need to be made to

obtain the desired shape. Consider the following principles:

Each cut creates two new edges.

The total perimeter of the material remains

constant.

The area of the material remains constant.

3. Stack the pieces together. Once the cuts have been

made, arrange the pieces together to form the desired shape.

Consider the following principles:

The edges of the pieces must match up.

The pieces must fit together without any gaps or

overlaps.

4. Check your solution. Make sure that the assembled

shape has the correct dimensions and satisfies the given

constraints.

Examples.

Example 1:

Starting material: Rectangle with sides 10 cm and 15

cm.

Cuts: Two cuts parallel to the 10 cm side, 3 cm apart.

Desired shape: Rectangle with sides 7 cm and 15 cm.

Solution:

Cut the rectangle into three strips: 3 cm, 7 cm, and 5

cm.

Stack the 7 cm and 5 cm strips side by side to form

the desired rectangle.

Example 2:

Starting material: Square with side 10 cm.

Cuts: Four cuts from each corner to the opposite

corner.

Desired shape: Square with side 5 cm.

Solution:

Cut the square into four triangles.

Stack the triangles together with their vertices at

the center to form a smaller square.

Tips.

Draw a diagram of the material and the cuts to

visualize the problem.

Use a ruler or compass to make accurate measurements.

Check your solution multiple times to ensure accuracy.

中文回答：

压强切割和叠加问题的解题思路。

压强切割和叠加问题是指对一片材料进行一系列切割，然后将

剩余的碎片堆叠在一起，形成具有给定尺寸和形状的形状的物理学

问题。这类问题可以通过逻辑和几何知识的结合来解决。

关键概念。

压强切割，向材料施加力，使其沿特定线断裂的切割。

叠加，将材料碎片叠放在一起以形成所需形状的过程。

周长，形状边界的总长度。

面积，形状所占用的空间量。

对称性，具有镜像或多个镜像的形状。

解题步骤。

1. 理解给定信息。仔细阅读问题并找出以下信息：

初始材料的形状和尺寸。

切割的次数和位置。

所需最终产品的形状和尺寸。

2. 确定必要的切割。使用给定信息找出获取所需形状所需的切

割。考虑以下原则：

每一次切割都会产生两个新的边缘。

材料的总周长保持不变。

材料的面积保持不变。

3. 将碎片叠加在一起。切割完成后，将碎片叠加在一起以形成

所需的形状。考虑以下原则：

碎片的边缘必须匹配。

碎片必须无间隙、重叠地拼合在一起。

4. 检查你的解法。确保拼装后的形状具有正确的尺寸并满足给

定的约束条件。

示例。

示例 1：

初始材料，边长为 10 厘米和 15 厘米的长方形。

切割，平行于 10 厘米侧，间隔 3 厘米的两条切割线。

所需形状，边长为 7 厘米和 15 厘米的长方形。

解法：

将长方形切割成三条带，3 厘米、7 厘米和 5 厘米。

将 7 厘米和 5 厘米的条带并排叠加以形成所需的长方形。

示例 2：

初始材料，边长为 10 厘米的正方形。

切割，从每个角到对角的四条切割线。

所需形状，边长为 5 厘米的正方形。

解法：

将正方形切割成四个三角形。

将三角形的顶点叠放在中心处，拼成一个较小的正方形。

提示。

绘制材料和切割的示意图以可视化问题。

使用尺子或圆规进行精确测量。

多次检查你的解法以确保准确性。