Vincent Green stared at the crumpled analytics report in his hand, his expression a mixture of confusion and dismay. As the founder of Green Innovations, a company specializing in sustainable technology, he had envisioned a company that not only provided viable environmental solutions but also communicated effectively with its audience. Yet, the report clearly showed that their social media influence was negligible, engaging with an audience far removed from their target demographic.

The company's recent campaign had flopped, targeting retirees rather than environmentally conscious millennials. The platform they chose, ElderChat, was popular among the older generation but wasn't frequented by the young activists and tech-savvy consumers Vincent intended to reach.

Moreover, the campaign's central theme, 'Legacy,' failed to resonate. It was intended to emphasize the long-term impact of sustainable choices, but instead, it came across as ill-suited for a youthful audience who were more engaged with current and relatable eco-challenges.

Lost in thought, Vincent's gaze landed on a book left open on his desk. The non-descript mathematics book had a page facing up, serendipitously displaying the formula for calculating the circumference of a circle using pi. Something about the simplicity and universality of the formula sparked an idea in Vincent's mind.

Eureka! If his company's communication could embody the concept of pi—endless, constant, and universally understood—it might create a strategy as resonant as the number itself. A strategy that acts like the circles it represented, reaching outward in all directions yet always leading back to the core—Green Innovations.

Vincent realized the essence of communication wasn't just the message, but also the method by which it perpetually expanded, reaching further, involving more. He envisioned a series of stories, testimonials, and interactive sessions revolving around the company's core mission but expanding like ripples in a pond.

The first step was to re-center. Green Innovations would realign with current issues—the immediate concerns daunting environmental enthusiasts. The 'Sustainable Now' series would launch, highlighting cutting-edge innovations, youthful eco-warriors, and actionable advice for immediate impact.

Next, Vincent decided to switch platforms. The message would circle out through InstaViral, frequented by millennials, using #GreenCircleGrows to encapsulate their spreading influence.

To solidify their rebranding, the 'GreenXChangemakers' conference was announced, an annual event bringing together the brightest minds to discuss and collaborate on environmental innovations—with live broadcasts and interactive sessions on multiple social media platforms.

Within months, the buzz was palpable. The circle was indeed growing, enfolding experts, enthusiasts, and curious onlookers into its embrace. Vincent smiled at the nifty infographic tracing the spike in engagement. All channels, all demographics, all dialogues led back to Green Innovations—just as he had hoped.

Vincent reflected on the journey. He had started with a message lost in translation and transformed it into a compelling dialogue. The company now stood not just as a beacon of innovation but also as a hub of positive engagement, an exemplar of how the right circle of communication could encompass the globe.

Taking a moment to ponder over their success, Vincent knew that their communication strategy would always evolve, just like the infinite possibilities of pi. He realized that the true power lay in the perpetual motion of ideas, circling out, yet staying connected, creating an enduring legacy of change.