Whether or not you've previously employed the golden ratio, artists like Salvador Dali and Le Corbusier have sworn by its aesthetic pleasure for nearly a century and a half. Its inception, however, dates back 2,300 years, where it can be found Euclid's Elements.
Here's the mathematical definition: two objects are in the golden ratio if their ratio equals the ratio of their sum to the larger of the two quantities. After the math, if you get a value of 1.6180, then these two objects fall within the golden ratio.
The golden ratio locates the proportional perfection in your surroundings.
The most famous application of the golden ratio, however, is the golden rectangle—a shape which can be split into a perfect square and a smaller rectangle that has the same aspect ratio as the rectangle from which it was cut.
Now, the design company Areaware has created a pocket-sized golden rectangle that can be used as a viewfinder to find the golden ratio.
Areaware's Golden Section Finder
“Historically, artists, designers, and architects have used [the golden ratio] as a means of defining beauty in a theoretical rather than intuitive way,” says the product's description. “Use the Golden Section Finder, a pocket-sized gazing device, to locate the proportional perfection in your surroundings.”
Areaware's Golden Section Finder
Even if you don't believe in the legitimacies of the golden ratio, you can try out the Golden Section Finder here in either blue or yellow for $10, or pick both up as a bundle for just $18. For that kind of cash, it's at least worth experimenting.
For a little over two hours, I was glued to my seat in the AMC Century City, fascinated and entralled in the world of the tennis dramaChallengers.
This masterful movie, directed by Luca Guadagnino and starring Zendaya, Mike Faist, and Josh O'Connor, is sexy, unflinching, and leaves audiences pondering its final moments.
The film, filled with flashbacks and unspoken emotions, culminates in a high-stakes match between childhood friends Art and Patrick, vying for a win that transcends the scoreboard. But the true victory, the movie suggests, lies elsewhere.
Let's explore.
Spoilers for the movie Challengers to come...
Challengers Movie Summary
In the movie Challengers, Tashi, a former tennis star turned coach, sees her husband Art, a once-dominant professional player, sinking into a slump.
Seeking to restore his fire, she enters him in a low-level "Challenger" tournament, expecting easy wins. However, her plan unravels when Art faces his estranged childhood friend and Tashi's ex-boyfriend, Patrick, whose own career has fizzled into mediocrity.
This unexpected reunion throws the trio's intertwined past into stark relief, revealing a history of intense friendship, youthful ambition, romantic entanglements, and unspoken betrayals.
As flashbacks weave through the present, Challengers explores the fragility of male friendship, particularly when fueled by competition, ambition, and a shared love for the same woman.
These flashbacks also expose the sacrifices Tashi made when her promising tennis career was cut short by injury. And how Art took care of her, and married her. But her passion for Patrick still burned hot, and their love triangle got even more complicated.
The focus of the film culminates in the climactic match between Art and Patrick. This battle transcends sport—it becomes a raw, physical confrontation with a past they cannot outrun.
In the final frames, they're playing a tie breaker, going back and forth.
So what happens next?
Challengers Ending Explained
Director Luca Guadagnino opts for an ambiguous ending, leaving the final point of the match unseen.
Art, fueled by a revelation of past betrayal, unleashes his fury on the court.
Patrick, seeking redemption, battles back.
The tension reaches a fever pitch as Art lunges for a final shot, colliding with Patrick in a tangle of limbs as he dives over the actual net and into his arms.
This isn't just a tennis maneuver; it's a physical manifestation of their complex bond.
And it symbolizes the reuniting of their friendship.
Their embrace is open to interpretation, but my take is that it hints at a long-awaited forgiveness. Art and Patrick, despite years of estrangement, may be rediscovering a connection forged on the tennis courts of their youth.
Of course, this could be more complicated since Tashi has recently slept with Patrick, but maybe not.
Tashi adds another layer to the ending. Is her enthusiastic cheer a sign of renewed passion for the game, or is it fueled by the raw emotion displayed on the court?
Her future with Art remains uncertain. She respects him as a father but wants him to want to be a tennis player, the thing that was taken away from her.
In the final scene, they are finally communicating, not with words, but through the language of the game that brought them together.
Whether Art emerges victorious, or Patrick claims his comeback, is ultimately irrelevant. The ending of Challengers is a dance of forgiveness, a tentative step towards healing old wounds. And perhaps, that's the most satisfying victory of all.
Guadagnino told Entertainment Weekly he kept the winner ambiguous on purpose: "I needed to get this very, very visually amped up and really immersed for the audience to understand how much it meant for them not to win over the other, but to be back together, all of them."
The question of which guy Tashi chooses at the end is also on the audience's mind.
Writer of the movie Justin Kuritzkes told Indie Wire “I chose to end the movie where I ended the movie, and I chose to end it there because for me, the movie is over. For me, what’s going on with these people has resolved in some way that’s satisfying enough for me. And I always want to start a movie as late as possible and end a movie as early as possible. So for me, I got what I needed by then, and I feel like they did too.”
Challengers is a film that lingers, like the echo of a well-struck ball. It doesn't offer easy answers, preferring to explore the complexities of human connection and the weight of the past.
Whether Art or Patrick ultimately triumphed on the court is less important than the journey they took to reach that point, a journey that may forever change the dynamics of their tangled relationship with Tashi.
Is tennis the ultimate key to forgiveness? Let me know what you think in the comments.