Mathomat V3

# The Hidden Geometry in the Opal Card Logo

video tutorial part
16
of

## Exploring the geometry of the Opel card with a Circle Arc Template

with

### Chris Tisdell

Mathematician & Educator

### Materials you will need:

Mathomat V3 Template
Unlined Paper / Scrap Paper
Sharp Pencil/s
Fine-point Pen/s
Eraser

### What you will learn in this tutorial:

In this video, Chris Tisdell dives into the intriguing world of geometry, sparked by an everyday item we might overlook:the Opal card. He embarks on a fascinating journey of discovery, exploring the hidden geometric elements within the Opal card's logo and how they connect to ancient mathematical concepts.

#### Introduction: The Opal Card Logo

Chris begins by introducing the Opal card, a familiar sight for many in Sydney and parts of New South Wales. He highlights the captivating geometric aspects hidden within its logo, prompting him to explore this intriguing connection between everyday logos and geometry.

#### Analyzing the Opal Card Logo: A GeometricPerspective

To delve deeper, Chris dissects the Opal card logo, which primarily consists of a circle with curved elements inside.However, there's more to it than meets the eye. He begins by introducing pointsA, B, C, and D within the logo, forming a square that's inscribed in the circle.

#### Exploring the Crescent Moon Shapes

Chris zooms in on the crescent-shaped"Moon" elements within the logo. He reveals a fascinating connection between these crescent Moon areas and a particular triangle, which he promises to unveil shortly.

#### Notation and Geometry: The Math Behind the Magic

To formalise his exploration, Chris introduces notation, marking the centre of the circle as point O and other points along the logo. He categorises areas within the logo, labelling them A1,A2, and A3, each corresponding to different regions.

#### The Key Insight: Equating Areas

Chris unveils a pivotal insight—the area of the triangle (A1) is equal to the area of the crescent Moon (A3). This revelation takes us back in time to an ancient problem in geometry, where mathematicians first discovered connections between curved and rectilinear shapes.

#### Comparing Areas of Different Shapes

Chris elaborates on this connection, showing that A1 + A2 equals the area of the quarter circle, while A2 + A3equals the area of the semicircle. The key takeaway is that the triangle's area equals that of the crescent Moon, providing a profound geometric connection.

#### The Quarter Circle vs. The Semicircle

Chris discusses the comparison between a quarter circle and a semicircle, shedding light on how this geometry relates to the Opal card logo. He expresses his fascination with this revelation, emphasising that it's not unique to the logo but appears in various forms across logos and designs.

#### Closing Thoughts

Chris wraps up his exploration by inviting viewers to share their thoughts and experiences with similar geometric connections in logos. He acknowledges that geometry plays a significant role in branding and design, making us appreciate the hidden mathematical beauty in everyday symbols.

In this video, Chris Tisdell not only deciphers the geometry behind the Opal card logo but also showcases the enduring relevance of mathematical principles in everyday life, bridging ancient discoveries with contemporary design.

### Chris Tisdell

Mathematician & Educator
Chris, a mathematician and educator, is an academic advisor to Mathomat. Chris approached us in 2021 with an interest in the circle templates in Mathomat...
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