Perfect Number
Seemingly an ordinary math teacher in high school, Suk-go is indeed a brilliant mathematician. Hwa-sun is his neighbor. They become inseparable when Suk-go decides to cover up Hwa-sun's accidental murder while she was mercilessly beaten by her ex-husband.
The film earned $10.2M at the global box office.
Plot Structure
Story beats plotted across runtime
Narrative Arc
Emotional journey through the story's key moments
Story Circle
Blueprint 15-beat structure
Arcplot Score Breakdown
Weighted: Precision (70%) + Arc (15%) + Theme (15%)
Perfect Number (2012) demonstrates carefully calibrated narrative design, characteristic of Pang Eun-jin's storytelling approach. This structural analysis examines how the film's 15-point plot structure maps to proven narrative frameworks across 2 hours. With an Arcplot score of 6.3, the film takes an unconventional approach to traditional narrative frameworks.
Structural Analysis
The Status Quo at 1 minutes (1% through the runtime) establishes Ishigami, a brilliant but reclusive mathematics teacher, lives a quiet, solitary life governed by routine and intellectual pursuits, isolated from meaningful human connection.. Of particular interest, this early placement immediately immerses viewers in the story world.
The inciting incident occurs at 15 minutes when Yasuko's ex-husband arrives and attacks her; in the struggle, Yasuko and her daughter kill him in self-defense, creating a crisis that shatters their lives.. At 12% through the film, this Disruption aligns precisely with traditional story structure. This beat shifts the emotional landscape, launching the protagonist into the central conflict.
The First Threshold at 30 minutes marks the transition into Act II, occurring at 25% of the runtime. This demonstrates the protagonist's commitment to Ishigami commits fully to his plan, disposing of the body and constructing an elaborate mathematical deception to protect Yasuko, crossing the point of no return., moving from reaction to action.
At 60 minutes, the Midpoint arrives at 50% of the runtime—precisely centered, creating perfect narrative symmetry. Significantly, this crucial beat Yukawa begins to suspect his old friend Ishigami is involved, raising the stakes from a routine investigation to a personal confrontation between two brilliant minds. The game becomes dangerous., fundamentally raising what's at risk. The emotional intensity shifts, dividing the narrative into clear before-and-after phases.
The Collapse moment at 90 minutes (75% through) represents the emotional nadir. Here, Yukawa deduces the horrifying truth: the body found wasn't the ex-husband, and Ishigami sacrificed an innocent homeless man to create the perfect mathematical alibi. The magnitude of Ishigami's devotion is revealed., reveals the protagonist at their lowest point. This beat's placement in the final quarter sets up the climactic reversal.
The Second Threshold at 95 minutes initiates the final act resolution at 80% of the runtime. Yasuko decides to confess the truth to save Ishigami from his self-destruction, choosing moral responsibility over the freedom he tried to give her. She understands the true cost of his devotion., demonstrating the transformation achieved throughout the journey.
Emotional Journey
Perfect Number's emotional architecture traces a deliberate progression across 15 carefully calibrated beats.
Narrative Framework
This structural analysis employs a 15-point narrative structure framework that maps key story moments. By mapping Perfect Number against these established plot points, we can identify how Pang Eun-jin utilizes or subverts traditional narrative conventions. The plot point approach reveals not only adherence to structural principles but also creative choices that distinguish Perfect Number within the crime genre.
Comparative Analysis
Additional crime films include The Bad Guys, Batman Forever and 12 Rounds.
Plot Points by Act
Act I
SetupStatus Quo
Ishigami, a brilliant but reclusive mathematics teacher, lives a quiet, solitary life governed by routine and intellectual pursuits, isolated from meaningful human connection.
Theme
A colleague or student discusses the concept of sacrifice and devotion in mathematical proofs, foreshadowing the film's exploration of how far one will go for love.
Worldbuilding
Establishment of Ishigami's methodical existence, his genius-level intellect, his neighbor Yasuko and her daughter, and the oppressive presence of Yasuko's abusive ex-husband who threatens their safety.
Disruption
Yasuko's ex-husband arrives and attacks her; in the struggle, Yasuko and her daughter kill him in self-defense, creating a crisis that shatters their lives.
Resistance
Ishigami discovers the murder and, driven by his hidden love for Yasuko, offers to help cover up the crime. He debates internally but his devotion overrides hesitation as he meticulously plans the perfect alibi.
Act II
ConfrontationFirst Threshold
Ishigami commits fully to his plan, disposing of the body and constructing an elaborate mathematical deception to protect Yasuko, crossing the point of no return.
Mirror World
Detective Yukawa, Ishigami's former university colleague and intellectual equal, is brought onto the case, representing the rational world that will challenge Ishigami's emotional sacrifice.
Premise
The cat-and-mouse game between Ishigami's perfect logical construct and Yukawa's investigation unfolds. Ishigami stays steps ahead while maintaining his facade, and Yasuko remains unknowingly protected.
Midpoint
Yukawa begins to suspect his old friend Ishigami is involved, raising the stakes from a routine investigation to a personal confrontation between two brilliant minds. The game becomes dangerous.
Opposition
Yukawa closes in on the truth while Ishigami's plan begins to show cracks. Yasuko grows suspicious of Ishigami's help and starts to pull away, even as the police pressure intensifies.
Collapse
Yukawa deduces the horrifying truth: the body found wasn't the ex-husband, and Ishigami sacrificed an innocent homeless man to create the perfect mathematical alibi. The magnitude of Ishigami's devotion is revealed.
Crisis
Ishigami faces the emotional devastation of his plan's exposure and Yasuko's horror at what he's done in her name. His sacrifice, meant as an act of love, becomes a burden of guilt.
Act III
ResolutionSecond Threshold
Yasuko decides to confess the truth to save Ishigami from his self-destruction, choosing moral responsibility over the freedom he tried to give her. She understands the true cost of his devotion.
Synthesis
The confession unfolds and Ishigami's complete plan is laid bare. The mathematical perfection of his crime is matched only by the tragedy of his unrequited love and wasted genius.
Transformation
Ishigami is led away in custody, his face showing both devastation and a strange peace, having finally expressed his love through the ultimate sacrifice, though it destroyed him.