Visualization with GInMA in geometry teaching

Vladimir Shelomovskii, Svetlana NosulyaRussia

GInMA in geometryThis Workshop is focused on the aspect of visualization in geometry teaching. We consider visualization with GInMA software, its features and benefits. We use visualization as a basic tool in study of all major geometric topics. At the end of the Workshop you may create interactive draft on your own.

GInMA for teachingprovides visualization and

deeper understanding

of mathematics.

GInMA for researchbroadens opportunities

to perform interactive research

in the field of mathematics.

GInMA idea

We have made DGS and Library of more than 800 examples and samples.

Users start from PDF,

explore geometric drafts in shareware, make and save files in payware.

Installation, shareware

To make geometric drafts alive, install the program from the website

deoma-cmd.ru.

Click Geometry button on Main page, or GInMA button on the panel to download GInMA software.

Shareware is free

Use "GInMA installation guide"

GInMA support, GInMA Library

On Geometry page use the link "GInMA brief user manual" which helps you to use images in GInMA files and control them.

On Geometry page use the link "GInMA User Manual" which helps you to make complicated constructions on your own.

GInMA Library includes more than 800 interactive drafts. Click on the figures and investigate interactive constructions.

Active point, point with parents,

a segment, directed segment,

a ray, a line, perpendicular lines,

a circle,

an arc, the sign of the angle,

a triangle, a polygon,

a plane, normal plane,

a sphere,

a cylinder,

a cone,

text

GInMA: Basic construction

Use the adequate formula to create

a point, directed segment,

a segment, a ray, a line,

a circle,

a plane,

a sphere,

a curve (function),

truncated sphere,

truncated cylinder,

a surface.

GInMA: Analytic construction

Use the transformation to create

homothetic,

centrosymmetry,

axial symmetry,

plane symmetry,

translation,

inversion.

GInMA: Transformations

GInMA for teaching

Visualization of a flexible polyhedron

A flexible polyhedron is a polyhedral surface that allows continuous non-rigid deformations such that all faces remain rigid. Let us consider the Connelly flexible polyhedron, consisting of 18 triangular faces.

GInMA for teaching

Illustration of the solid of intersection. You can use it for explanation geometric methods

used to find the extremum in geometry.

The center of the unit cube is the apex of the quadrant. Find the least volume of the cube within the quadrant.

Illustration of the cross-sections. We may use it to explain the geometric methods of the cross-section construction.

GInMA for teaching

Illustration of the angles between lines and planes.

GInMA for teaching

GInMA for teaching

Cavalieri's principle in GInMA Library.

Axis of revolution replacement

Figure of revolution replacement

GInMA for teaching GInMA Library shows: Orthotomics

Pedal surface

Caustics

Evolute

GInMA for teaching

Visualization of 3D motion to develop spatial imagination. Moving of the object on the screen is organized in a comfortable way.

GInMA for teaching

Samples of polyhedronsSamples allow you to supplement the images in the drafts of the set and to create your own interactive constructions. You may save your constructions

after purchasing the set.

Regular Tetrahedron

Regular triangular pyramid

Cube

Prism, right triangle in base

Truncated pyramid

GInMA for research

SejfriedianGiven any reference ABC triangle. Let’s construct three pairs of lines.

The lines AA1, BB1 and CC1 intersect at three points K1, L1 and M1.

The lines AA2, BB2 and CC2 intersect at three points K, L and M.

If points K1, L1, M1, K, L, and M belong to one circle, then:

the pair of the triangles KLM and K1L1M1 have been called Sejfried triangles,

the circle KLM have been called Sejfried circle,

the center of Sejfried circle have been called Sejfried point,

all this construction have been called Sejfriedian.

Find Sejfriedian for given triangle.