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| /// Represents a point in 4D space | |
| #[derive(Debug, Clone, Copy)] | |
| struct Point4D { | |
| x: i32, | |
| y: i32, | |
| z: i32, | |
| w: i32, | |
| } | |
| impl Point4D { | |
| /// Calculates the squared Euclidean distance from the origin (0,0,0,0) | |
| fn distance_squared(&self) -> i32 { | |
| self.x.pow(2) + self.y.pow(2) + self.z.pow(2) + self.w.pow(2) | |
| } | |
| /// Returns the Euclidean distance as a f64 | |
| fn distance(&self) -> f64 { | |
| (self.distance_squared() as f64).sqrt() | |
| } | |
| } | |
| fn main() { | |
| let target_sq = 7; | |
| let search_range = 0..3; // Searching within 3 units in each dimension | |
| println!("--- Tesseract Coordinate Explorer ---"); | |
| println!("Searching for vertices that satisfy x² + y² + z² + w² = {}\n", target_sq); | |
| let mut found_any = false; | |
| for x in search_range.clone() { | |
| for y in search_range.clone() { | |
| for z in search_range.clone() { | |
| for w in search_range.clone() { | |
| let point = Point4D { x, y, z, w }; | |
| let dist_sq = point.distance_squared(); | |
| if dist_sq == target_sq { | |
| found_any = true; | |
| println!( | |
| "FOUND: Vertex ({}, {}, {}, {}) -> distance: √{} (≈ {:.4})", | |
| x, y, z, w, dist_sq, point.distance() | |
| ); | |
| if w == 0 { | |
| println!(" [!] Warning: This vertex exists in 3D space."); | |
| } else { | |
| println!(" [+] This vertex requires the 4th dimension (w-axis)."); | |
| } | |
| } | |
| } | |
| } | |
| } | |
| } | |
| if !found_any { | |
| println!("No integer vertices found for √{} in this range.", target_sq); | |
| } else { | |
| println!("\nMathematical Note:"); | |
| println!("Legendre's three-square theorem proves that 7 cannot be the sum"); | |
| println!("of 3 integer squares. By adding the 4th dimension (w), we can"); | |
| println!("reach √7 using coordinates like (2, 1, 1, 1)."); | |
| } | |
| } |
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