Table of Contents

**What is Geometry?**

Geometry is the branch of math that deals with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. In a broader sense, geometry is the study of any kind of shape or structure.^{1} Geometry arose independently in several early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with *Elements* being the first known text to codify this knowledge. Greek geometry was systematized by Euclid in his *Elements* while he drew on earlier works of Eudoxus of Cnidus and Theaetetus.^{2}

**What are the Basic Principles of Geometry?**

Geometry is the branch of math that deals with the properties and relations of points, lines, angles, surfaces, and solids. The word “geometry” comes from the Greek words for “earth” and “measurement.” Geometry is a broad field that has its roots in ancient times.^{3}

The earliest known recordings of geometry date back to 3700 BCE, in the form of Babylonian cuneiform tablets.^{4} One of the most famous geometricians of antiquity was Euclid, who lived in Alexandria around 300 BCE. Euclid’s work Elements codified many of the basic principles of geometry and is still studied by students today.^{2}

**How can Geometry be Used to Solve Real-world Problems?**

Geometry is a branch of math that deals with the study of shapes and figures.^{1} It is a very useful tool that can help us solve many real-world problems. For instance, imagine you want to build a fence around your property. You will need to know the lengths of the sides of your property to calculate the amount of fencing material you need. This is where geometry comes in handy.

By using geometry, you can easily calculate the lengths of the sides of your property and determine how much fencing material you need. In another example, let’s say you are a carpenter and you need to cut a piece of wood into a certain shape.

**What are Some Common Geometry Problems?**

There are a variety of geometry problems that students may encounter in their math classes. One common problem is finding the area of shapes. This can be done by using formulas or by breaking the shape down into smaller pieces and adding up the areas of the individual parts. Another common problem is finding the volume of a three-dimensional object.

This can be done by using formulas or by slicing the object into thin pieces and adding up the volumes of the individual slices. Other common geometry problems include finding the perimeter of a shape and calculating the surface area of a 3D object. With practice, students will be able to master these and other geometry concepts.

**How to Use Geometry to Solve a Problem?**

There are many ways to use geometry to solve problems. One way is to use a ruler or measuring tape to measure the length of an object. Another way is to use a protractor to measure angles. You can also use a compass to draw circles or arcs. Often, you will need to use more than one of these methods to solve a problem. For example, if you are trying to find the area of a square, you will need to use a ruler or measuring tape to measure the length of one side, and then multiply that by the length of the other side.

To find the circumference of a circle, you will need to use a compass to draw the circle, and then use a ruler or measuring tape to measure the distance around the circle. There are many other ways to use geometry to solve problems, and often the best way to figure out how to solve a problem is to experiment with different methods until you find one that works.

**Tips for Using Geometry to Solve Problems**

Geometry can be a helpful tool for solving problems in many different areas of math. For example, when working with fractions, geometry can be used to visualize and understand relationships between numbers. Geometry can also help solve word problems by visualizing the situation and identifying the relevant information.

In addition, geometry can be used to solve problems in physics by helping to visualize objects and their interactions. These are just a few of the many ways that geometry can be used to solve problems. With a little creativity, geometric concepts can be applied to almost any type of problem.

**5 Common Applications of Geometry in the Real World**

1. **Architecture**: The study of geometry is essential for any aspiring architect. From planning the layout of a building to designing its facade, geometry is used at every stage of the architectural process.^{5}

2. **Interior** **design**: Geometry can also be used to create beautiful and functional living spaces. By understanding the principles of space and proportion, interior designers can create rooms that are both aesthetically pleasing and practical.^{6}

3. **Landscaping**: The shapes and sizes of plants and trees must be taken into account when designing a landscape. By using geometry, landscapers can create gardens that are visually stunning and easy to maintain.^{7}

4. **Engineering**: Geometry is a vital tool for any engineer, whether they are designing a bridge or a skyscraper. The properties of geometric shapes must be taken into account to ensure that a structure is stable and safe.^{8}

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**References**

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*Euclidean Geometry*. Euclidean Geometry. Retrieved November 30, 2022, from https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/non_Euclid_Euclid/index.html - Etymonline. (2018, October 31).
*geometry | Etymology, origin and meaning of geometry by etymonline*. Geometry | Etymology, Origin and Meaning of Geometry by Etymonline. Retrieved November 30, 2022, from https://www.etymonline.com/word/geometry - Turner, L. (2021, August 7).
*Babylonians used Pythagorean theorem 1,000 years before it was “invented” in ancient Greece*. livescience.com. Retrieved November 30, 2022, from https://www.livescience.com/earliest-form-of-pythagorean-triplet - Saraf, T. (2020, July 5).
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*5 Ways Geometry is Used in Interior Design*. Ldb-interior-design. Retrieved November 30, 2022, from https://www.ldbdesign.com/post/2016-07-18-5-ways-geometry-is-used-in-interior-design - Carpenter. (2017, September 26).
*The Ways Geometry Is Used in Gardening | Homesteady*. HomeSteady | the Ultimate Guide for All Your Household Needs. Retrieved November 30, 2022, from https://homesteady.com/info-8502917-ways-geometry-used-gardening.html - St. Clair. (2021, August 3).
*Civil Engineers use math to design, build and maintain transportation structures | ADOT*. Civil Engineers Use Math to Design, Build and Maintain Transportation Structures | ADOT. Retrieved November 30, 2022, from https://azdot.gov/adot-blog/civil-engineers-use-math-design-build-and-maintain-transportation-structures