## Irina Boyadzhiev - My GeoGebra Applets

Categories:

- ♦ Geometry
- ♦ Trigonometry
- ♦ Conic Sections
- ♦ Algebra, Precalculus and Calculus
- ♦ The Limaçon
- ♦ Optimization Problems
- ♦ Bézier Curves
- ♦ The Equiangular Spiral and Fibonacci Numbers
- ♦ Series
- ♦ Number Sense - Fractions
- ♦ Geometry for K-9 Teachers
- ♦ Catacaustics

## New

- Circumference of a Circle and Pi, April 2015
- Trigonometric Functions with Variable Amplitude, Feb. 2015
- Graphs of Trigonometric Functions, Feb. 2015
- Coterminal and Reference Angles, Feb. 2015
- Radians, Number Line and the Unit Circle, Jan. 2015
- Visual Proof – a fraction between two given fractions
- Golden Triangles and Infinite Series , March 2014
- Line Symmetries and the Quadrilaterals Feb. 2014
- Midsegments and Congruent Triangles, Jan. 2014

## Geometry

- Construction Vs Drawing Oct. 2009
- Midsegmens and Congruent Triangles, Jan. 2014
- The Area of the Median Triangle - Dynamic Proof, Jan. 2014
- Dynamic Proof of Equal Areas, Dec. 2013

- The Law of Cosines, Dec. 2013

- The Nine-point Circle Oct. 2009
- Medians and Triangles with Equal Area Oct. 2009
- Intersecting Secants Theorem 2010

## Some Geometry Problems

## Trigonometry

- Radians, Number Line and the Unit Circle, Jan. 2015
- Trigonometric Functions with Variable Amplitude, Feb. 2015
- Graphs of Trigonometric Functions, Feb. 2015
- Coterminal and Reference Angles, Feb. 2015

## Conic Sections

- Conic Sections - A Geometric Construction using the Eccentricity 2010, Modified Feb. 2014
- Geometric Construction of a Hyperbola and an Ellipse with Asymptotes and Directrixes 2010, Modified Feb. 2014

## Algebra, Precalculus and Calculus

- Domain and Range of a Function, Jan 2013
- Domainand Range of a Function by Flattening to the Axis, Jan 2013

- Vertical
Line Test
, Sept. 2013

- Inverse Function , Sept.2013
- Horizontal Line Test , Sept. 2013

## The Limaçon

- Limaçon as a Roulette - 1 Nov. 2010

## Optimization Problems

- Rectangle with maximum area if the perimeter is fixed Oct. 2009
- Rectangle with Maximum Area inscribed in a triangle Oct. 2009; Modified Jan. 2014
- An Isosceles Triangle with Fixed
Perimeter
, Sept.2013

- Area of an Isosceles Triangle with Fixed Two Equal Sides,
Sept. 2013

## Bézier Curves

- Bézier Curves - Equations , Apr. 2012 Modified Jan. 2014
- Bezier Curves - Recursive Construction , Apr. 2012; Modified Jan. 2014
- Poly-Bézier curves, Dec. 2014

## The Equiangular Spiral and Fibonacci Numbers

- GeoGebra construction of an Equiangular Spiral - 1 2010
- GeoGebra construction of the Pedal and Copedal curve of an Equiangular Spiral 2010
- Measuring Equiangular Spirals in Nature 2010,
update
March 2012

- GeoGebra investigation of the Equiangular Spiral in Plants; Fibonacci Numbers , March 2012
- Building of Fibonacci squares and Fibonacci Spiral,
March 2012

- Fibonacci Spiral -
demonstration
, March 2012

- GeoGebra investigations of equiangular spirals in the flight of insects Nov. 2011

## Series

- Golden Triangles and Infinite Series , March 2014
- Infinite
Geometric Series - Sum of Areas of Triangles
,
May 2013

- The Sum of the First n Natural Numbers - Dynamic Geometric Proof , March 2013
- Arithmetic Series - Dynamic Geometric Proof , March 2013
- The Sum of the Cubes of the First N Natural Numbers , April 2013
- The Sum of Squares - Dynamic Geometric Proof , Feb. 2013
- The sum of the first N odd numbers , March 2013

## Number Sense - Fractions

- Fractions, Feb. 2013
- Equivalent Fractions - One Common Misconception , Feb. 2013

## Geometry for K-9 Teachers

- Triangles with Equal Area
- Definition of a Circle, Jan. 2014
- Dynamic Proof of the Pythagorean Theorem
- Properties
of Parallelograms
, Oct. 2013

- Theorems and Postulates for Congruent Triangles , March, 2012; Modified Jan. 2014
- The sum of the acute angles in a right triangle
- The Sum of the Interior Angles of a Triangle, Jan. 2014
- The sum of the interior angles in Any Triangle by Rotation and Translation
- The Sum of the Exterior Angles of Any Triangle
- Line Symmetries and the Quadrilaterals Feb. 2014

## Some Simulations

- Rolling a rectangle; Perimeter 2011
- Rolling a Circle -Circumference of a Circle, an Approximation of π, Radian Measure Oct. 2011

## Arc Bound Squarable Shapes

## Catacaustics

- Catacaustic of a Circle - Parallel Rays Oct. 2011
- Catacaustic of a Circle - Radial Rays Oct. 2011
- Catacaustic of an Ellipse - Parallel Rays Oct. 2011
- Catacaustic of an Ellipse - Radial Rays Oct. 2011
- Catacaustic of a Parabola - Parallel Rays Tschirnhausen Cubic Oct. 2011
- Catacaustic of a Parabola - Parallel Rays Oct. 2011
- Catacaustic of a Parabola - Radial Rays Oct. 2011
- Catacaustic of a Hyperbola - Radial Rays Oct. 2011
- Catacaustic
of a Hyperbola - Parallel Rays
Oct. 2011