100 Examples of sentences containing the common noun "isometry"

Definition

Isometry refers to a transformation in geometry that preserves distances between points. In a broader mathematical context, isometry can also denote any mapping that maintains the metric structure of a space, ensuring that distances remain unchanged.

Synonyms

• Distance-preserving transformation
• Rigid motion
• Congruence transformation

Antonyms

• Distortion
• Non-isometric transformation
• Deformation

Examples

1. The isometry of the triangle ensured that all sides remained equal after the transformation.
2. Mathematicians often study isometry to understand the properties of geometric shapes.
3. In computer graphics, an isometry can help maintain the proportions of objects during rendering.
4. The concept of isometry is crucial in proving the congruence of geometric figures.
5. When you apply an isometry to a shape, it does not change its size or form.
6. Understanding isometry is essential for advanced studies in differential geometry.
7. The isometry between these two spaces demonstrates their equivalence in terms of distance.
8. Using an isometry, you can rotate a figure without altering its dimensions.
9. The isometry of the circle is different from that of the square due to their unique properties.
10. In topology, an isometry is a function that preserves the topology of the space.
11. Engineers use isometry to ensure structural integrity in designs.
12. The isometry between the two graphs illustrated their similarity.
13. An isometry can be represented by a combination of translations and rotations.
14. The study of isometry has applications in robotics and motion planning.
15. A common example of isometry is a reflection across a line.
16. The isometry of the cube allows for various symmetrical transformations.
17. In physics, isometry can describe the conservation of distances during motion.
18. The isometry mapping was visually represented in the software.
19. You can verify the isometry of two shapes by measuring their corresponding sides.
20. The isometry in the experiment showed that the two materials behaved similarly under stress.
21. A proper isometry must satisfy the condition of distance preservation.
22. The isometry applied to the polygon resulted in a congruent shape.
23. In advanced mathematics, the concept of isometry is extended to higher dimensions.
24. The isometry of the function can be used to simplify complex problems.
25. During the transformation, the isometry kept all angles intact.
26. The isometry ensures that the original structure is maintained throughout the transformation.
27. In computer-aided design, understanding isometry is crucial for accurate modeling.
28. The isometry of the graph was crucial in the analysis of its properties.
29. A reflection is an example of an isometry that can be easily visualized.
30. The mathematician proved that the isometry was valid for all points in the plane.
31. The isometry was instrumental in demonstrating the theorem.
32. By applying an isometry, we can find the image of a shape under transformation.
33. The concept of isometry is foundational in the study of metric spaces.
34. The isometry can be represented using matrices in linear algebra.
35. The use of isometry in the design process enhanced the project’s accuracy.
36. With every isometry, the overall structure remains unchanged.
37. Understanding isometry can help in visualizing complex transformations.
38. The isometry between the two figures was confirmed through geometric proofs.
39. The principle of isometry can simplify many mathematical calculations.
40. The isometry preserved the original distances in the model.
41. In an isometry, the center of rotation plays a key role in the transformation.
42. During the study, an isometry was identified as a crucial factor.
43. The isometry helped in mapping the original shape to a new coordinate system.
44. The isometry illustrated how distances are maintained even during rotation.
45. Learning about isometry can enhance one's understanding of geometric relationships.
46. The isometry allowed for the creation of a mirror image without distortion.
47. When teaching geometry, it's important to highlight the concept of isometry.
48. The isometry between the two curves was evident from their measurements.
49. A series of isometry transformations can lead to complex patterns.
50. The isometry in the model ensured that each segment remained equal.
51. In the analysis, the isometry was essential for validating the results.
52. The isometry transformation can be visualized through dynamic geometry software.
53. The isometry preserved the relationships between the vertices of the shape.
54. A fundamental property of isometry is that it does not alter angles.
55. The mathematician showcased various examples of isometry in her lecture.
56. The isometry facilitated the understanding of spatial relationships.
57. By examining the isometry, we can deduce the properties of the shape.
58. The isometry proved that the two triangles were congruent.
59. An isometry does not change the orientation of the shape.
60. The isometry mapping was created using rigorous mathematical techniques.
61. The isometry between the two different shapes highlighted their equivalence.
62. Understanding the properties of isometry is vital for geometry students.
63. The isometry maintained the integrity of the design throughout the process.
64. The application of isometry in this context yields interesting results.
65. The isometry allowed for a seamless transition from one shape to another.
66. Learning about isometry can enhance problem-solving skills in geometry.
67. The concept of isometry can be applied in various fields, including architecture.
68. The isometry maintained the proportions in the scaled model.
69. A comprehensive understanding of isometry is necessary for advanced mathematics.
70. The isometry technique can be used in both two-dimensional and three-dimensional spaces.
71. The isometry demonstrated that the two shapes were indeed congruent.
72. By applying isometry, we can derive valuable insights about the space.
73. The isometry preserved the triangle's dimensions during the transformation.
74. The properties of isometry are crucial for understanding geometric proofs.
75. In the study of algebraic structures, isometry plays a significant role.
76. The isometry allows for a clear comparison between different mathematical objects.
77. The isometry confirmed that the measurements were accurate.
78. Understanding isometry can lead to better design practices in engineering.
79. The isometry showed how the shape reacted to different transformations.
80. The isometry preserved the distances, making it a useful tool in geometry.
81. In calculus, isometry can help in analyzing functions and their properties.
82. The isometry technique is often used in computer simulations.
83. The isometry mapping was essential for the analysis of the data set.
84. The isometry helped in visualizing abstract concepts in geometry.
85. The isometry provided a consistent framework for the transformation.
86. By using isometry, we can easily compare two shapes for congruence.
87. The isometry illustrated the importance of distance preservation in mathematics.
88. The principle of isometry was applied in the construction of the model.
89. The isometry ensured that the final design met the required specifications.
90. The isometry played a key role in the study of geometric transformations.
91. The properties of isometry can be explored through various mathematical tools.
92. The isometry provided a clear understanding of the shapes involved.
93. By applying an isometry, the mathematician was able to simplify the proof.
94. The concept of isometry extends to various branches of mathematics and science.
95. The isometry was a fundamental aspect of the geometric analysis.
96. A reflection is one of the simplest forms of isometry.
97. The isometry mapping ensured that the results were consistent across trials.
98. The understanding of isometry can greatly enhance one's analytical skills.
99. The isometry confirmed the equivalence of the two geometric figures.
100. By studying isometry, we can gain insight into the nature of distance in geometry.