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Discover how intuitive geometry can be when you keep your assumptions simple and use your own logic and reasoning to set up your calculations.
This fundamentals course will introduce you to angle axioms, perimeter and area calculation strategies, coordinate geometry, 3D geometry, and more. This is the course that you should begin with if you're just starting your exploration of geometry on Brilliant.
Some prior experience with algebra is assumed, but you're in good shape to start this course if you can plot points and linear equations on a coordinate plane and use a variable to describe the relationship between the side length of a square and its area.
And, by the end of this course, you’ll be a skilled geometric problem-solver, well practiced at everything from proving the Pythagorean theorem to mixing algebraic and geometric techniques together on the coordinate plane.
Overview
Syllabus
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- Introduction: Cuts, folds, and rearrangements — see how hands-on manipulation of shapes can reveal the truth without a calculation.
- Calculating Area: Geometry is a way of thinking — sometimes a new perspective can save a calculation.
- Cutting Shapes: Slice and dice to make reasoning about shapes more intuitive.
- Angles in Polygons: Reason your way from basic angle properties to a universal truth of triangles.
- Angles and Lengths: Angle and length — geometry's basic units of measure — are tools in the detective hunt to characterize new shapes.
- Angle Facts: Build up a toolbox of angle ideas to discover geometric principles.
- Triangle Sides and Angles: Sides and angles — the unbreakable partnership that makes triangles what they are today.
- Angle Hunting: Put your knowledge of angles to work to track down the missing information in these shape puzzles.
- Perimeters: Trace the borders of your understanding by exploring the paths around shapes.
- Circumference and Arc Lengths: How long is a circle?
- Area: From the circle to the pyramid, the area of many shapes can be found by building them out of rectangles.
- Polygon Areas: How many squares do we need to build a triangle?
- Circles: How many triangles do we need to build a circle?
- Composite Figures: To conquer new shapes, it helps to catch a glimpse of the old.
- Surface Area: How much paint do we need to redecorate a prism?
- Pyramids and Cones: Pinch your understanding of prisms to find the surface area of pyramids and cones.
- Pythagoras' Geometry: Discover the famous law of right triangles using the power of perspective, and learn how to apply it in several different contexts.
- The Pythagorean Theorem: Unlock Pythagoras’ famous formula by looking at the same triangle in two different ways.
- Applying the Pythagorean Theorem: If at first you can't see a triangle in your problem, you might not be looking hard enough.
- Coordinate Geometry: Overlay a grid and any problem can be a geometry problem.
- Coordinate Distance: With a grid and Pythagoras, we can find any distance.
- Scaling and Volume: With area as a base, use symmetry and slice to find the volume of shapes.
- Volume: How many cubes do we need to build a cylinder?
- Pyramids and Cones: Through symmetry and slice, discover the volume of these solids without an ounce of calculus.
- Geometric Ratios: How do the pieces of a shape relate to one another?
- Similarity: Can we use our knowledge of one shape to find the measurements of another?
- Scaling: How do geometric properties change as a shape grows?
- When Geometry Gets Tough: Apply what you’ve learned to these challenging problems.
- Finding Triangles: You'll need to use some triangular tricks to solve these problems.
- Relating Parts to the Whole: When faced with a complex figure, consider the part each piece plays.
- Advanced Angle Hunting: Use the rules you've learned to chase down every angle in sight.
