12th Grade Shapes Interactive Videos

Explore the calculation of hydrostatic force on a tank by applying integral calculus and principles of similarity triangles. Develop skills to calculate hydrostatic forces and understand fundamental fluid mechanics concepts, enhancing problem-solving abilities in physics and engineering.

Exploration of trigonometry and geometry highlights the importance of the Law of Sines and Cosines in architectural design. Learners will enhance their problem-solving abilities and deepen their understanding of mathematical relationships that are vital for effective architectural planning and construction.

Focus on the fundamental characteristics of three-dimensional geometric figures by identifying vertices, edges, and faces. Develop a clear understanding of these components to enhance spatial reasoning skills and geometric knowledge.

Explore the concept of cross sections in geometry by understanding how slices of three-dimensional shapes result in two-dimensional figures and analyzing the transformations caused by rotations. Develop the ability to identify and describe the two-dimensional shapes produced by various cuts, enhancing spatial reasoning and comprehension of geometric properties.

Utilizing geometric reasoning in higher dimensions enhances learners' spatial intuition and analytical capabilities, allowing them to comprehend complex mathematical concepts involving multidimensional spaces.

Explore the world of 3D modeling by designing nonlinear shapes using various CAD tools. Develop skills in creating complex models and master advanced design techniques to enhance proficiency in computer-aided design applications.

Discover the extraordinary mathematical journey of Kelsey Johnson and Nakia Jackson as they engage with ancient puzzles at St. Mary's Academy. Their innovative use of trigonometric proofs demonstrates a groundbreaking approach that highlights the importance of a nurturing educational environment in developing mathematical skills and achieving excellence.

Calculate the perimeter of composite figures by exploring various two-dimensional shapes. Develop geometry skills by understanding and applying techniques for finding perimeters, building confidence in managing complex figures effectively.

Examine the fundamentals of three-dimensional coordinate systems, highlighting the introduction of the z-axis and the concept of octants. Gain proficiency in visualizing and interpreting points in 3D space, thus enhancing overall comprehension of mathematical concepts in multidimensional analysis.

Explore the intriguing concept of constant width shapes, including Reuleaux triangles, and discover their unique geometric properties. Gain an understanding of their application in real-world scenarios to enhance knowledge of geometry and engineering concepts.

Understand the components and volume calculations of 3D shapes, focusing on cones and their segments. Gain insight into the relationships between different parts of a cone and the process of computing and analyzing volume ratios. Enhance problem-solving skills in geometry through these calculations and analyses.

Explore the fundamental role of different shapes in design, including their categories, meanings, and impacts on visual perception. Understanding how shapes can symbolize concepts such as wholeness or hierarchy enhances the ability to apply design principles effectively.

Examine foundational concepts and address common misconceptions about the Big Bang Theory, concentrating on the visualization of an expanding universe. Gain a deep understanding of essential principles, such as the implications of a universe without edges, and how these insights underpin modern cosmological models. Develop comprehension of the universe’s continuous expansion and how this theory integrates into contemporary scientific understanding.

Understand and explore perimeter and area concepts in composite shapes, focusing on geometry fundamentals and enhancing problem-solving skills. Master the calculation of perimeters in complex shapes and develop an understanding of geometric properties, equipping learners with essential skills for advanced geometry studies.

Explore the intriguing concepts of quaternions and their visualization through stereographic projection. Gain a comprehensive understanding of quaternion properties and their role in 3D rotations, enhancing advanced algebra and geometry skills.

Explore the fascinating world of parametric surfaces through the use of complex functions and mathematical visualization techniques. Enhance your understanding of geometric patterns and learn how functions can be applied to create intricate shapes, such as the torus.

Explore the geometric challenge of calculating angles between lines and planes in triangular prisms through 3D trigonometry. Develop proficiency in applying Pythagoras' Theorem and tangent functions to solve complex geometric problems, enhancing analytical skills within mathematical contexts. Demonstrate the ability to apply mathematical principles effectively and accurately in practical situations.

Investigate the geometric reasoning involved in visualizing problems in higher dimensions, emphasizing spatial reasoning and understanding. Gain insights into advanced visualization techniques and learn how these concepts can improve your ability to address complex multidimensional geometric challenges.

Explore the fundamental differences between shapes and forms in visual arts. Enhance understanding of how these elements convey emotions and messages effectively in diverse artistic practices.

Gain a comprehensive understanding of three-dimensional coordinate systems by focusing on axes and projections. Develop essential skills in interpreting and visualizing 3D objects and coordinate planes, thereby enhancing the comprehension of multivariable calculus applications.