58

Signed-off-by: Jess Frazelle <[email protected]>

Author: jessfraz

results/prompt_58.md

@@ -0,0 +1,91 @@
+# Prompt #58: A 4×2 rectangle lies flat on the xy-plane. It is tilted 30° toward you (rotation about the x-axis). Draw a simple 2-line ASCII perspective of the resulting trapezoid (front edge vs. back edge).
+
+## OpenAI o3  (12 secs)
++--------+      (front edge)
+  +------+      (back edge, raised & slightly foreshortened)
+
+## Claude 4 Sonnet  (5 secs)
+Looking at a 4×2 rectangle tilted 30° toward you (rotation about the x-axis), here's the ASCII perspective view:
+
+```
+    --------
+   /        /
+  /        /
+ ----------
+```
+
+The bottom line (front edge) appears longer than the top line (back edge) due to perspective. The front edge is closer to you at full width (4 units), while the back edge appears shorter due to foreshortening from the 30° tilt.
+
+## Gemini Pro  (23 secs)
+Okay, let's visualize this:
+
+1.  **Original Rectangle:**
+    *   Width (along x-axis): 4 units
+    *   Depth (along y-axis): 2 units
+
+2.  **Tilt:**
+    *   Rotation is about the x-axis by 30° "toward you."
+    *   This means the edge that was originally at y=0 (the "front" edge closest to you if you're looking down the y-axis) stays at y=0, z=0.
+    *   The edge that was originally at y=2 (the "back" edge) will now have:
+        *   A new y-coordinate (depth from your viewpoint): `2 * cos(30°) ≈ 2 * 0.866 = 1.732`
+        *   A new z-coordinate (height above the xy-plane): `2 * sin(30°) = 2 * 0.5 = 1`
+
+3.  **Perspective:**
+    *   The front edge (width 4) is closer, so it appears its full width.
+    *   The back edge (actual width 4) is further away (at y ≈ 1.732) and higher up (at z = 1). In a perspective view, things further away appear smaller.
+
+4.  **ASCII Representation:**
+    *   We need two lines. The top line will represent the back edge, and the bottom line will represent the front edge.
+    *   The front edge should be wider.
+    *   The back edge should be shorter and centered above the front edge.
+
+Let's represent the front edge (width 4) with, say, 12 characters: `------------`
+The back edge (actual width 4, but appearing shorter due to perspective) should be noticeably shorter. Let's make it, say, 8 characters: `--------`
+
+To make it look like a trapezoid, the back edge needs to be centered relative to the front edge.
+Front edge length: 12
+Back edge length: 8
+Difference: 4 characters. So, we need 4/2 = 2 spaces on either side of the back edge.
+
+```ascii
+  --------  <-- Back edge (further away, higher up, appears shorter)
+------------  <-- Front edge (closer, on the original plane, appears wider)
+```
+
+This gives a simple representation of the trapezoidal shape formed by the front and back edges after the tilt and with perspective applied.
+
+## DeepSeek Reasoner  (437 secs)
+The rectangle is initially positioned on the xy-plane with corners at (0,0,0), (4,0,0), (0,2,0), and (4,2,0). After a 30° rotation about the x-axis towards the viewer, the front edge (originally at y=0) remains at (x,0,0) for x from 0 to 4, and the back edge (originally at y=2) moves to (x, 1.732, 1.0) for x from 0 to 4, using √3/2 ≈ 0.866 and sin(30°) = 0.5.
+
+For the perspective projection, the camera is placed at (2, -d, 0) with d = √3 ≈ 1.732 to achieve a size ratio of 2:1 between the front and back edges. The projection uses a view plane at y=0. After scaling to fit an 8-character width for the front edge in ASCII:
+
+- The front edge (bottom row) spans 8 characters: `--------`.
+- The back edge (top row) is half the size (4 characters) and centered, resulting in 2 spaces on each side: `  ----  `.
+
+This shows the trapezoid shape with the front edge longer and closer (bottom) and the back edge shorter and farther (top), as viewed from the front with perspective.
+
+ASCII representation:
+```
+  ----  
+--------
+```
+
+- **Top line**: Back edge, shorter and centered (4 dashes with 2 spaces on each side).
+- **Bottom line**: Front edge, full width (8 dashes).
+
+This simple 2-line ASCII art captures the perspective of the tilted rectangle as a trapezoid, emphasizing the size difference due to depth.
+
+## Grok 3  (3 secs)
+Here's a simple 2-line ASCII representation of the 4×2 rectangle tilted 30° toward you (rotation about the x-axis). When tilted, the rectangle appears as a trapezoid in perspective due to the foreshortening of the y-dimension. The front edge (closer to you) remains the full width, while the back edge (farther away) appears narrower.
+
+```
+   /--------\
+  /----------\
+```
+
+- The bottom line represents the front edge (closer to you), which is the full width of 4 units (scaled roughly by the number of dashes).
+- The top line represents the back edge (farther away), which appears shorter due to perspective after the 30° tilt.
+- The slanted sides (`/` and `\`) indicate the convergence of the sides toward the back, mimicking the trapezoidal shape in perspective.
+
+This is a basic approximation, as ASCII art is limited, but it captures the essence of the front edge being wider than the back edge due to the tilt.
+