Use the following Media4Math resources with this Illustrative Math lesson.
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Closed Captioned Video: Geometry Applications: 3D Geometry |
Closed Captioned Video: Geometry Applications: 3D Geometry In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures. — CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Closed Captioned Video: Geometry Applications: 3D Geometry, 1 |
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 1: Introduction. We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures. — CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these figures. Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms. |
3-Dimensional Figures and Applications of 3D Geometry | |
Closed Captioned Video: Geometry Applications: 3D Geometry, 2 |
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 2: Pyramids Rectangular Prisms. Mayan pyramids are essentially stacks of rectangular prisms. The volume of each successive level is a percentage decrease of its lower neighbor. This introduces the notion of a geometric sequence and series, including an infinite series. — CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these figures. Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms. |
3-Dimensional Figures, Pyramids and Applications of 3D Geometry | |
Closed Captioned Video: Geometry Applications: 3D Geometry, 3 |
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series. — CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these figures. Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms. |
3-Dimensional Figures, Cylinders and Applications of 3D Geometry | |
Geometry Applications Teachers Guide: 3D Geometry |
Geometry Applications Teachers Guide: 3D Geometry
This is the Teacher's Guide that accompanies Geometry Applications: 3D Geometry. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of 3D Geometry | |
Holiday Math Clip Art--Candy Box |
Holiday Math Clip Art--Candy BoxTopicGeometry DescriptionThis holiday-themed math clip art features a festive candy box, offering a delightful blend of seasonal cheer and geometric concepts. The image can be broken down into its fundamental geometric components, showcasing both 2D and 3D elements. In 2D, the candy box presents a cardioid shape, resembling a heart or rounded triangle. This unique curve can be explored in terms of its properties and equations. The box's decorative elements, such as bows or patterns, may incorporate additional 2D shapes like circles, ovals, or polygons. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Candy Cane |
Holiday Math Clip Art--Candy CaneTopicGeometry Description
This holiday-themed math clip art showcases a classic candy cane, a perfect subject for exploring various geometric concepts. The candy cane's distinctive shape offers rich opportunities for analyzing both 2D and 3D geometric elements. In 2D, the candy cane can be broken down into rectangles and semicircles. The straight part of the cane forms a rectangle, while the curved hook at the top creates a semicircle. This allows for discussions about properties of these shapes, such as area calculations and the relationship between a semicircle's diameter and its arc length. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Candy Mint |
Holiday Math Clip Art--Candy Mint
This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects. To see the complete collection of these images, click on this link. Note: The download is a PNG file.Math Clip Art LibraryTo see the complete Math Clip Art Library, click on this link. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Chocolate Bar |
Holiday Math Clip Art--Chocolate Bar
This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects. To see the complete collection of these images, click on this link. Note: The download is a PNG file.Math Clip Art LibraryTo see the complete Math Clip Art Library, click on this link. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Chocolate Candy |
Holiday Math Clip Art--Chocolate CandyTopicGeometry DescriptionThis holiday-themed math clip art features chocolate candy, providing an excellent opportunity to explore geometric concepts in both 2D and 3D contexts. The simplicity of the candy's shape belies the rich mathematical discussions it can inspire. In 2D, the chocolate candy presents as a perfect circle. This allows for exploration of circular properties such as diameter, radius, circumference, and area. The candy's surface design, which may include patterns or decorations, can introduce concepts like symmetry, geometric transformations, or even basic trigonometry if the designs include angular elements. |
Size, 3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Christmas Tree |
Holiday Math Clip Art--Christmas TreeTopicGeometry DescriptionThis holiday-themed math clip art showcases a Christmas tree, offering a festive way to explore various geometric concepts in both 2D and 3D contexts. The tree's distinctive shape provides rich opportunities for mathematical analysis and discussion. In 2D, the Christmas tree can be broken down into a triangle for the main body and a rectangle for the trunk. This allows for exploration of properties such as angles, base, height, area, and perimeter. The decorations on the tree can introduce concepts of symmetry, patterns, and even coordinate geometry if we imagine the ornaments as points on a plane. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Dreidel |
Holiday Math Clip Art--DreidelTopicGeometry DescriptionThis holiday-themed math clip art features a dreidel, a traditional Hanukkah toy that offers a unique opportunity to explore geometric concepts in both 2D and 3D contexts. The dreidel's distinctive shape provides a rich foundation for various mathematical discussions. In 2D, the dreidel can be broken down into several shapes. The body presents as a square or rectangle, the top as a smaller rectangle, and the point at the bottom as a triangle. This allows for exploration of properties such as angles, sides, area, and perimeter. The Hebrew letters on each face introduce concepts of symmetry and rotational transformations. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Drum |
Holiday Math Clip Art--DrumTopicGeometry DescriptionThis holiday-themed math clip art features a festive drum, offering an excellent opportunity to explore geometric concepts in both 2D and 3D contexts. The drum's simple yet distinctive shape provides a rich foundation for various mathematical discussions. In 2D, the drum can be broken down into basic shapes. The top and bottom of the drum present as circles, while the side forms a rectangle. This allows for exploration of properties such as diameter, radius, circumference, and area for circles, as well as length, width, and perimeter for rectangles. The decorative elements on the drum's surface can introduce concepts of symmetry and patterns. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Gift Box |
Holiday Math Clip Art--Gift Box
This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects. To see the complete collection of these images, click on this link. Note: The download is a PNG file.Math Clip Art LibraryTo see the complete Math Clip Art Library, click on this link. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Gingerbread House |
Holiday Math Clip Art--Gingerbread HouseTopicGeometry DescriptionThis holiday-themed math clip art features a gingerbread house, offering a delightful way to explore geometric concepts in both 2D and 3D contexts. The gingerbread house's structure provides a rich foundation for various mathematical discussions, combining architectural elements with festive design. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Gingerbread Man |
Holiday Math Clip Art--Gingerbread ManTopicGeometry DescriptionThis holiday-themed math clip art showcases a gingerbread man, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The gingerbread man's shape provides a unique opportunity to discuss various geometric forms and their combinations. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Candy Corn |
Holiday Math Clip Art--Halloween--Candy CornTopicGeometry DescriptionThis Halloween-themed math clip art features candy corn, offering a seasonal way to explore geometric concepts in both 2D and 3D contexts. The distinctive shape of candy corn provides an excellent opportunity to discuss various geometric forms and their properties. In 2D, candy corn is typically represented as a triangle. This allows for exploration of properties such as angles, base, height, area, and perimeter. The three-color design of candy corn also introduces the concept of dividing a triangle into smaller triangles, which can lead to discussions about similarity and proportions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Chocolate Bar |
Holiday Math Clip Art--Chocolate BarTopicGeometry DescriptionThis holiday-themed math clip art showcases a chocolate bar, offering a delightful way to explore geometric concepts in both 2D and 3D contexts. The chocolate bar's simple yet structured shape provides an excellent foundation for various mathematical discussions. In 2D, the chocolate bar presents as a rectangle. This allows for exploration of properties such as length, width, perimeter, and area. The individual chocolate squares within the bar create a grid, introducing concepts of arrays, rows, and columns. This grid structure can also be used to discuss fractions and ratios. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Lollipop |
Holiday Math Clip Art--Halloween--LollipopTopicGeometry DescriptionThis Halloween-themed math clip art features a lollipop, offering a sweet way to explore geometric concepts in both 2D and 3D contexts. The lollipop's simple yet distinctive shape provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Mint |
Holiday Math Clip Art--Candy MintTopicGeometry DescriptionThis holiday-themed math clip art features a festive candy mint, providing an excellent opportunity to explore geometric concepts in both 2D and 3D contexts. The simplicity of the mint's shape belies the rich mathematical discussions it can inspire. In 2D, the candy mint presents as a perfect circle. This allows for exploration of circular properties such as diameter, radius, circumference, and area. The mint's surface design, often featuring spirals or radial patterns, can introduce concepts like rotational symmetry and geometric transformations. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Moon |
Holiday Math Clip Art--Halloween--MoonTopicGeometry DescriptionThis Halloween-themed math clip art features a moon, offering a celestial way to explore geometric concepts in both 2D and 3D contexts. The moon's simple yet evocative shape provides a rich foundation for various mathematical discussions, particularly fitting for the spooky atmosphere of Halloween. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Pumpkin |
Holiday Math Clip Art--Halloween--PumpkinTopicGeometry DescriptionThis Halloween-themed math clip art showcases a pumpkin, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The pumpkin's distinctive shape provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Title Page |
Holiday Math Clip Art--Halloween--Title PageTopicGeometry DescriptionThis Halloween-themed math clip art features a title page, offering a spooky introduction to explore geometric concepts in both 2D and 3D contexts. While a title page might not immediately suggest geometric analysis, it provides an opportunity to discuss layout, design, and the geometric principles underlying visual communication. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Vampire Coffin |
Holiday Math Clip Art--Halloween--Vampire CoffinTopicGeometry DescriptionThis Halloween-themed math clip art features a vampire coffin, offering a spooky way to explore geometric concepts in both 2D and 3D contexts. The coffin's unique shape provides an excellent opportunity to discuss various geometric forms and their properties. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Halloween--Witch's Hat |
Holiday Math Clip Art--Halloween--Witch's HatTopicGeometry DescriptionThis Halloween-themed math clip art features a witch's hat, offering a spooky way to explore geometric concepts in both 2D and 3D contexts. The distinctive shape of the witch's hat provides an excellent opportunity to discuss various geometric forms and their properties. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Holiday Lights |
Holiday Math Clip Art--Holiday LightsTopicGeometry DescriptionThis holiday-themed math clip art features festive lights, offering a bright way to explore geometric concepts in both 2D and 3D contexts. The string of lights provides a unique opportunity to discuss various geometric forms and their combinations. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Lollipop |
Holiday Math Clip Art--Lollipop
This is part of a collection of math clip art images that take holiday images and render them as two- and three-dimensional geometric objects. To see the complete collection of these images, click on this link. Note: The download is a PNG file.Math Clip Art LibraryTo see the complete Math Clip Art Library, click on this link. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Lollipop 2 |
Holiday Math Clip Art--Lollipop 2TopicGeometry DescriptionThis holiday-themed math clip art features another representation of a lollipop, offering a different perspective on blending sweet imagery with mathematical precision. The image demonstrates how basic geometric shapes can be combined in various ways to create recognizable objects, reinforcing the connection between abstract geometry and everyday items. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--North Pole |
Holiday Math Clip Art--North PoleTopicGeometry DescriptionThis holiday-themed math clip art features a North Pole sign, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The North Pole sign provides a unique opportunity to discuss various geometric forms and their combinations. In 2D, the North Pole sign can be broken down into basic shapes. The pole itself is represented by a rectangle, while the the top is represented by a circle. This composition allows for exploration of properties such as length, width, area, and perimeter for rectangles, as well as diameter and circumference for circles. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Ornament |
Holiday Math Clip Art--OrnamentTopicGeometry DescriptionThis holiday-themed math clip art features a Christmas ornament, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The ornament's simple yet distinctive shape provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Present |
Holiday Math Clip Art--Gift BoxTopicGeometry DescriptionThis holiday-themed math clip art showcases a gift box, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The gift box's simple yet distinctive shape provides a rich foundation for various mathematical discussions. In 2D, the gift box can be broken down into basic shapes. The main body of the box is likely represented by a square or rectangle, while the ribbon and bow might be depicted using additional rectangles or curved shapes. This allows for exploration of properties such as length, width, area, and perimeter. The symmetry of the gift box design can also be a point of discussion. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Snow Globe |
Holiday Math Clip Art--Snow GlobeTopicGeometry DescriptionThis holiday-themed math clip art features a snow globe, offering a magical way to explore geometric concepts in both 2D and 3D contexts. The snow globe's unique shape provides an excellent opportunity to discuss various geometric forms and their combinations. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Snow Man |
Holiday Math Clip Art--Snow ManTopicGeometry DescriptionThis holiday-themed math clip art showcases a snowman, offering a delightful way to explore geometric concepts in both 2D and 3D contexts. The snowman's simple yet distinctive shape provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Snowflake |
Holiday Math Clip Art--SnowflakeTopicGeometry DescriptionThis holiday-themed math clip art features a snowflake, offering a beautiful way to explore geometric concepts primarily in 2D contexts. The snowflake's intricate and symmetrical shape provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Star |
Holiday Math Clip Art--StarTopicGeometry DescriptionThis holiday-themed math clip art showcases a star, offering a brilliant way to explore geometric concepts primarily in 2D contexts, with some interesting 3D applications. The star's distinctive shape provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Stocking |
Holiday Math Clip Art--StockingTopicGeometry DescriptionThis holiday-themed math clip art features a Christmas stocking, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The stocking's unique shape provides an excellent opportunity to discuss various geometric forms and their combinations. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Toy Soldier |
Holiday Math Clip Art--Toy SoldierTopicGeometry Description
This holiday-themed math clip art showcases a toy soldier, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The toy soldier's complex shape provides a rich foundation for various mathematical discussions, combining multiple geometric forms. |
3-Dimensional Figures and Applications of 3D Geometry | |
Holiday Math Clip Art--Wreath |
Holiday Math Clip Art--WreathTopicGeometry DescriptionThis holiday-themed math clip art features a wreath, offering a festive way to explore geometric concepts in both 2D and 3D contexts. The wreath's circular shape with its intricate details provides a rich foundation for various mathematical discussions. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Figures--Cube |
Math Clip Art--3D Figures--Cube
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Figures--Cylinder |
Math Clip Art--3D Figures--Cylinder
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Objects--Barrel |
Math Clip Art--3D Objects--Barrel
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Objects--Bowl |
Math Clip Art--3D Objects--Bowl
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Objects--Box |
Math Clip Art--3D Objects--Box
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Objects--Building |
Math Clip Art--3D Objects--Building
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--3D Objects--Cinder Block |
Math Clip Art--3D Objects--Cinder Block
This collection of clip art images includes images of 3D figures and composite figures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math Clip Art--Geometry Concepts--Cone |
Math Clip Art--ConeTopicGeometry Concepts DescriptionThis image illustrates a cone, a three-dimensional geometric shape with a circular base that tapers smoothly to a point called the apex. Cones are commonly seen in everyday objects such as ice cream cones and traffic cones. Understanding the properties of cones, such as their volume and surface area, is essential in geometry. The volume of a cone is calculated using the formula V = 1/3 πr2h, where r is the radius of the base and h is the height. The surface area includes the base area and the lateral surface area, which can be calculated using the formula A = πr(r + l), where l is the slant height. |
3-Dimensional Figures and Applications of 3D Geometry | |
Math in the News: Issue 42--The Burj Khalifa Tower |
Math in the News: Issue 42--The Burj Khalifa Tower
January 2012. In this issue we look at the Burj Khalifa Tower, made popular with the release of the Mission Impossible movie. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of 3D Geometry | |
Math in the News: Issue 87--The Wonders of 3D Printing |
Math in the News: Issue 87--The Wonders of 3D Printing
January 2014. In this issue of Math in the News we look at 3D printing technology. In particular, we look at Nike's recent unveiling of a new running shoe developed using 3D printing. Mathematically, we look at recursive functions, since the 3D printing technology was used for rapid, iterative prototyping of the new shoe. We look at an example of a recursive function, using the Babylonian method to calculate the square root of a number. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of 3D Geometry | |
Video Transcript: Geometry Applications: 3D Geometry |
Video Transcript: Geometry Applications: 3D Geometry
This is the transcript for the video of same title. Video contents: In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures. |
3-Dimensional Figures and Applications of 3D Geometry | |
Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction |
Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction
This is the transcript for the video of same title. Video contents: We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures. This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. |
3-Dimensional Figures and Applications of 3D Geometry |