THE PYTHAGOREAN THEOREM - The name makes it sound like something akin to advanced particle physics, but it's actually a fairly simple, straightforward way to calculate the length of the third side of a right triangle if you know the lengths of the other two sides. The equation that derives from the Pythagorean Theorem is familiar to many: a2 + b2 = c2. The Pythagorean Theorem holds that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It will help you to know how to calculate square roots, and you can also use basic algebra to figure out any missing side of a right triangle as long as you know two of its measurements.

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The Pythagorean Theorem

What Is the Pythagorean Theorem?

Wonderopolis

There are certain things you learn in school that you use on an everyday basis.

Some of these things include reading, writing, spelling, and basic mathematics, such as addition, subtraction, multiplication, and division.

Then there are other things that you learn in school that you probably don't use every single day.

How often do you need to know when World War I started?

Does knowing the details of the process of photosynthesis come in handy every day?

How about all those esoteric mathematical concepts and formulas?

Will algebra ever be useful in real life? Actually, you might be surprised how often you end up using algebra and other mathematical concepts without even realizing it.

Let's take a look at one of those formulas you may have learned about in school: the Pythagorean Theorem.

The name makes it sound like something akin to advanced particle physics, but it's actually a fairly simple, straightforward way to calculate the length of the third side of a right triangle if you know the lengths of the other two sides.

The equation that derives from the Pythagorean Theorem is familiar to many: a² + b² = c².

In this equation, c represents the longest side (known as the hypotenuse) of a right triangle.

Reminder: a right triangle is a triangle that has one 90˚ angle.

The letters a and b represent the other two sides.

Stated another way, the Pythagorean Theorem holds that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, if side a measures 3 and side b measures 4, you can calculate that side c will measure 5 (3² + 4² = 5² or 9 + 16 = 25).

It will help you to know how to calculate square roots, and you can also use basic algebra to figure out any missing side of a right triangle as long as you know two of its measurements.

The Pythagorean Theorem is credited to Pythagoras, who was a Greek philosopher and mathematician that lived in the 5^th century B.C.

However, historians have discovered that other ancient civilizations knew about the basic mathematics of the Pythagorean Theorem thousands of years earlier.

For example, new studies show that the ancient pillars of Stonehenge may have been placed very precisely using the geometry of the Pythagorean Theorem.

Although no one knows who built Stonehenge, historians believe it was constructed over 2,000 years before Pythagoras was born.

Does the Pythagorean Theorem have any usefulness in real life? You bet it does!

First, it's often used as the basis for more complicated mathematics, including calculating areas, volumes, and perimeters of all sorts of geometric shapes.

On a day to day basis, you might find yourself using the Pythagorean Theorem in certain types of jobs and tasks.

These might include architecture, construction, navigation, and surveying.

Basically, any time you build something and you need to use square angles or know how long one side of a triangle needs to be, you'll be using the Pythagorean Theorem!

·  Follow the link to learn how to use shoes to create triangles that you can then measure to confirm the Pythagorean Theorem. Have fun confirming what mathematicians have known for centuries!

·  Are you a sports fan? Check out The Pythagorean Theorem and Baseball online. Can you solve the puzzle? Apply what you've learned about the Pythagorean Theorem. You can click for a hint if you need one.

·  We don't condone breaking and entering, but sometimes you might find yourself locked out of the house and need to borrow a ladder to climb to a second story window to get in. Use the information in The Pythagorean Theorem and Ladders to solve a simple puzzle. Isn't it cool how you can figure out how long the ladder needs to be?

Wonderopolis was created by the National Center for Families Learning (NCFL) in 2010, and it has become one of the most popular education sites today. 

The National Center for Families Learning (NCFL) works to eradicate poverty through education solutions for families. Over our 29-year history, we have changed the lives of millions of families across the country by providing innovative programs, strategies, and resources that support learning, literacy, and family engagement in education. Engaging multiple generations together has been a fundamental and distinguishing aspect of our work, because we know this holistic approach creates a stronger impact and greater success for families. For more information, please visit familieslearning.org.

https://www.wonderopolis.org/wonder/what-is-the-pythagorean-theorem

BRIDGES AND GEOMETRY - Geometric design is important in bridge design. roperly used, geometric figures can create extremely strong bridges. Though some bridges may use more geometric concepts than others, all bridge designs evenly distribute weight for proper bearing. Truss bridges rely heavily on triangles. Used properly, triangles evenly distribute weight throughout the bridge. Instead of pushing straight down, the weight of an arch bridge is carried outward along the curve of the arch to the supports at each end. Connector plates are used to help strengthen connecting points on bridges. Symmetry is important in bridge design because the entire length of the bridge must be able to bear weight. An asymmetrical bridge can cause the bridge to collapse.

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Bridges And Geometry

Geometric Concepts Found in Bridges

By Jennifer Elrod

Different bridge designs can be found throughout the world. You can find truss, arch, cable, beam, suspension and cantilever bridges in different areas.

The type of bridge used largely depends on the distance it must cover and the amount of load it must bear.

Geometric design is important in bridge design. Properly used, geometric figures can create extremely strong bridges.

Though some bridges may use more geometric concepts than others, all bridge designs evenly distribute weight for proper bearing.

Triangles

Truss bridges rely heavily on triangles. Used properly, triangles evenly distribute weight throughout the bridge.

Triangles are used on the sides and sometimes even the top of the bridge.

The top of a truss bridge may have an "x" design, where four triangles create enough support to bear a great deal of weight.

Students can use simple wooden craft sticks to create a truss bridge strong enough for the teacher to stand on.

A well-designed bridge is less about the materials and more about the design.

Arches

Arches are used to create arch bridges.

According to PBS.org, "Arch bridges are one of the oldest types of bridges and have great natural strength. Instead of pushing straight down, the weight of an arch bridge is carried outward along the curve of the arch to the supports at each end."

It may be a one-arch bridge, or there may be several arches side by side to create the support needed.

Connector Plates

Connector plates are used to help strengthen connecting points on bridges.

A connector plate is most commonly shaped as either a square or a triangle. They are made of steel and bolted onto intersecting points on a bridge.

The shape of the plate adds strength to these areas of the bridge. When pressure is added to the point of intersecting, the connector plate distributes the pressure.

There are different-sized plates and most have a galvanized coating to help prevent rust corrosion.

Symmetry

Symmetry is a geometric concept that is used in bridge design. Symmetry is where one half of a figure is the mirror image of its other half.

Symmetry is important in bridge design because the entire length of the bridge must be able to bear weight. An asymmetrical bridge can cause the bridge to collapse.

Each arch on an arch bridge must be symmetrical. The triangles on a truss bridge must be symmetrical. Even the spacing on cable and suspension bridges must be even and symmetrical.

About the Author

I'm an experienced teacher with a degree in Multidisciplinary Studies-Human Learning. I've worked with various grade levels at different educational facilities. My expertise includes: lesson planning, curriculum development, child development, educational practices and parent involvement.

https://sciencing.com/geometric-concepts-found-bridges-8711435.html

TRIANGLES USED IN ARCHITECTURE - The two most common triangular forms used in architecture are equilateral and isosceles. Triangles are effective tools for architecture and are used in the design of buildings and other structures as they provide strength and stability. When building materials are used to form a triangle, the design has a heavy base and the pinnacle on the top is capable of handling weight because of how the energy is distributed throughout the triangle. This is why many residential homes have A-frames; it provides a sturdy structure. The most sturdy of the triangles are equilateral and isosceles; their symmetry aids in distributing weight.

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Triangles Used in Architecture

By Nicholas Ramos

Geometry and architecture are two disciplines that are fundamentally linked.

One of the most recognized geometric shapes is the triangle.

Triangles are identified by the three angles that are linked through line segments to form a three-sided shape.

The two most common triangular forms used in architecture are equilateral and isosceles.

Triangles and Architecture

Triangles are effective tools for architecture and are used in the design of buildings and other structures as they provide strength and stability.

When building materials are used to form a triangle, the design has a heavy base and the pinnacle on the top is capable of handling weight because of how the energy is distributed throughout the triangle.

This is why many residential homes have A-frames; it provides a sturdy structure.

The most sturdy of the triangles are equilateral and isosceles; their symmetry aids in distributing weight.

Equilateral Triangle

The equilateral triangle is by far the most common triangle used in architecture.

An equilateral triangle features three congruent sides and angles measuring 60 degrees on each corner. The lengths of the sides vary.

A common example of equilateral triangles used in architecture is the Pyramid Complex of Giza in Egypt.

Each of the four triangular sides that form the pyramids are equilateral triangles.

These are examples of the strength of the triangle in architecture as the pyramids have been standing for over 4,000 years.

Isosceles Triangle

Isosceles triangles, which have two equal sides, are also found in architecture throughout the world, especially in modern pyramidal architecture.

Isosceles triangles were used in the architecture of the East Building in the National Gallery of Art in Washington, D.C.

The building was designed by the famous architect I.M. Pei.

His architectural style featured the use of isosceles triangles and other geometric shapes.

The East Building was plotted on an oddly shaped piece of land.

Pei used an isosceles triangle also as the base of the building to accommodate the shape of the plot.

The Flatiron Building in New York City is one of the world’s groundbreaking skyscrapers.

This building is built on a triangular block in Manhattan, giving it a triangular shape, specifically, an isosceles. It has stood over 100 years, illustrating the strength of triangular architecture.

Scalene and Right Angle Triangles

A scalene triangle is one in which all sides are incongruent. Scalene triangles are not commonly found in architecture.

There is no symmetry in these triangles, causing an uneven distribution in weight. This is hazardous as one angle will have more weight and pressure placed on it than another.

Right angle triangles have one angle that is a perfect 90 degrees. These special triangles are not traditionally used in the structural characteristics of a building.

They are, however, vital to the construction and design of the building.

Right triangles are used to create perfect corners and straight lines. If the walls and corners of a building are crooked, the building also will be crooked.

Additional Information

Triangles are also used as adornments in architecture, not just in the foundational design.

In churches, triangular windows are often featured as window frames or in the stained glass, possibly representing the Holy Trinity.

The Hearst Tower in Manhattan uses triangular framing to add extra support for the tower and to frame the all-glass window structure; both equilateral and isosceles triangles are used.

About the Author

Nicholas Ramos was born in Washington, D.C. He is currently a journalism major in Georgia and plans to specialize in law. Ramos has been writing since 2009, specializing in fashion, travel and health.

https://sciencing.com/triangles-used-in-architecture-12084289.html