3D augmented reality (AR) book

Learning geometry has never been so exciting! Our book describes and illustrates the basics of plane and spatial geometry with pictures and ultra-modern multimedia.

There is no doubt that the shortest way to understanding geometry is through illustration. We are revolutionizing this with our book and our augmented reality content that can be displayed with our free application.

Trailer, contents

CONTENTS

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1. Basic Concepts

The building blocks of geometry, rays and line segments, and the definition of finite and infinite sets.

Multimedia content

Finite or infinite?

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2. Position report

Determination of the relative positions of spatial elements.

Multimedia content

The mutual position of the elements in space

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3. Angles in Space

Angles between lines, planes, and lines and planes, perpendicularity, and determination of angles in space.

Multimedia content

The angle between two planes

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4. Near and Far

Distances between points, lines and planes, units of measurement, and determination of the shortest distance.

Multimedia content

Use of units of measurement

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5. Locus in Geometry

Determination of specially positioned points and sets of points in the plane and in space.

Multimedia content

Locus of points in space

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6. Vectors

Vectors, their magnitude and direction, opposite vectors, and the sum and difference of vectors.

Multimedia content

Multiplying a vector by a scalar

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7. Planar Transformations

Basics of point transformations and congruence transformations: translation, rotation, line reflection and point reflection.

Multimedia content

Planar transformations

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8. Translation

Vector definition of translation and its distance-, angle- and orientation-preserving properties.

Multimedia content

Translation

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9. Reflection

Point and line reflection, fixed points, invariant lines, and the properties of the transformations.

Multimedia content

Reflection about a line in space

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10. Similarity

Similarity transformation, scale factor, reduction and enlargement, and ratios of length, area and volume.

Multimedia content

The similarity transformation

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11. The Plane as a Mirror

Reflection about a plane, fixed and invariant shapes, and the geometric properties of a plane mirror.

Multimedia content

Reflection about a plane in space

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12. Rotation about a Point

Rotation about a point, direction, angle, fixed point, and identity transformations.

Multimedia content

Rotation about a point

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13. Rotation in Space

Rotation about a line in space, rotation axis, fixed points, direction, and congruence properties.

Multimedia content

Rotation about a line in space

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14. Pythagorean Theorem

Pythagorean theorem, relations between sides of right triangles, proof, and Pythagorean triples.

Multimedia content

Illustration of the Pythagorean theorem

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15. Thales' Theorem

Thales’ theorem, its proof, inscribed angle subtended by a diameter, and applications of the theorem.

Multimedia content

Application of Thales’ theorem

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16. Theorems abuot (Tri)Angles

Altitude theorem, leg theorem, intercept theorem, related proportions, and the concept of the geometric mean.

Multimedia content

The theorem of parallel intercepting line segments

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17. Trigonometry

Trigonometric relations in right triangles: sine, cosine, tangent and cotangent functions.

Multimedia content

Representation of the sine and cosine trigonometric functions

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18. Laws of Sines and Cosines

Application of the laws of sines and cosines to determine sides and angles of any triangles.

Multimedia content

Treasure hunt exercise

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19. Quadrilaterals

Classification and properties of quadrilaterals: trapezium, parallelogram, rhombus, rectangle, deltoid and square.

Multimedia content

Perimeter and area of quadrilaterals

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20. Outside & Inside

Properties of cyclic and tangential quadrilaterals and the related geometric theorems.

Multimedia content

Constructing the circumcircle of a quadrilateral

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21. Polygons

Characteristics of polygons, diagonals, interior and exterior angles, and properties of regular polygons.

Multimedia content

The area of a regular polygon

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22. Polyhedra

Polyhedra, Euler’s polyhedral formula, and the characteristics of regular solids.

Multimedia content

Solving a math problem: Octahedron

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23. Prisms

Definition and parts of prisms, and calculation of their surface area and volume.

Multimedia content

Derivation of a prism

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24. Right & Oblique

Comparison of right and oblique prisms, and differences in determining their surface area, height and volume.

Multimedia content

The surface area of a right prism

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25. On Quadrilateral Bases

Calculation of surface area and volume of special right prisms with quadrilateral bases, with a practical example.

Multimedia content

The square prism

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26. From Column to Cube

Properties, surface area and volume of square prisms and cubes, with a practical Rubik’s Cube example.

Multimedia content

The volume of a cube

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27. Pyramid

Definition and parts of pyramids, their derivation, right and oblique pyramids, surface area and volume formulas.

Multimedia content

The volume of a pyramid

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28. Truncated Pyramid

Definition and parts of truncated pyramids, surface area and volume, and application of similarity rules.

Multimedia content

The surface area of a truncated pyramid

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29. Circles

Basic circle concepts: circumference, radius, diameter, tangent, secant, chord, and calculation of circumference and area.

Multimedia content

The circumference and area of the circle

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30. Inside the Circle

Parts of a circle: disc, annulus, sector, segment and semicircle, and determination of their areas.

Multimedia content

Relationships in the circle

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31. Angles in the Circle

Central and inscribed angles, their corresponding arcs, and the relations between them.

Multimedia content

Measuring angles

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32. Spheres

Characteristics of spheres and spherical surfaces, radius, diameter, and determination of surface area and volume.

Multimedia content

The surface area of a sphere

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33. Is the Earth a Sphere?

Geometric relations between the sphere and Earth, geographical coordinates, latitude and longitude.

Multimedia content

The volume of a sphere

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34. (Circular) Cylinders

Definition of cylinders, types and parts of circular cylinders, and formulas for surface area and volume.

Multimedia content

The circular cylinder

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35. Cones

Parts of cones and cones of revolution: generator, lateral surface, base, and determination of surface area and volume.

Multimedia content

Volume of a circular cone

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36. Cones of Revolution

Geometric properties of cones of revolution generated by rotating axially symmetric plane figures.

Multimedia content

The surface area and volume of nested cones

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37. Cross Sections of a Cone

Plane sections of cones of revolution: circle, ellipse, parabola and hyperbola, plus truncated-cone derivation and surface area.

Multimedia content

The volume of a truncated cone

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38. "Spun" around

Solids of revolution generated by rotating plane figures around a symmetry axis, and examination of their volumes.

Multimedia content

How heavy is the ball?

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39. Inscribed Solids

Archimedes’ theorem, and the concept and characteristics of dual solids.

Multimedia content

Spheres inscribed in a cuboid

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40. A Solid in a Solid

Joined geometric solids, Platonic solids, and the stellated octahedron.

Multimedia content

A sphere inscribed in a cone

Try it for free!

Install the free app by scanning the QR code or clicking the appropriate store button, and experience the joy of learning through augmented reality.

In the app, tap the plus icon, select “Free trial publications”, then press the download button. Once the download is complete, start the demo by pressing the play button.

Using an older Android device? Click here to open the test page!.

Specification

ISBN 978-615-81881-8-0

Age recommended: 10+

Language: English

Number of pages: 90 pages

Size: B5

Quality: 4+4 colour printing spiral binding, inside sheet: 120 g offset paper; cover: 255 g GC1 cardboard, B1 and B4 matt coated

Number of AR elements: 40 3D holograms

Usage device: mobile phone or tablet

Operating System:

iOS: Devices running iOS 16, iPadOS 16 or later.
Android: Minimum Android 10 or later device with a 64-bit processor and operating system. Some features require an ARCore supported device.

Required device storage: 200 MB

Internet connection: Internet connection is required to download, run and update the application and play the content of the publication (WiFi connection recommended).

How it works?

Each page of the 40-topic publication features a special image, which triggers the corresponding AR video on the screen when scanned with a mobile device camera. 3D holograms are used to show the spatial and plane geometry. These multimedia contents explain geometric concepts and theorems through narration in addition to the visual presentation.

Who is it for?

Geometry has created for those who are learning about it at school or are simply interested in angles, vectors and shapes. The app that comes with the book is easy to use. You can simply download it from the AppStore or Google Play store, then launch and add the content of the publication using the code on the inside cover of the printed book. After that you can start playing augmented reality videos.

Geometry

19.80€

+ 3.10€ shipping

Free shipping on orders of 4 or more books.

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