Euler's Identity 欧拉恒等式

Euler's Identity, often celebrated as one of the most beautiful equations in mathematics because it connects five fundamental constants — (e), (i), (π), (1), and (0) — along with the fundamental operations of addition, multiplication, and exponentiation.

The Euler formula, sometimes also called the Euler identity (e.g., Trott 2004, p. 174), states

The special case of the formula with x=π gives the beautiful identity

Euler's formula has wide applications in mathematics, physics, and engineering. In physics, it is used to describe the relationship between rotation and frequency, and it serves as an indispensable foundational tool in signal processing and electrical engineering, such as in the analysis of three-phase circuits.

Dimensions after assembly: approx 280*161*170mm

组装后尺寸约280*161*170mm

This model enables visual observation of the mapping relationships among rotation, sine and cosine.

Two‑color filament is recommended for printing the end‑point spheres, which display different colors when viewed from various angles.

Either motor‑driven or manual assemblies can be printed as an option.

Non‑3D‑printed parts: 2× 608 bearings, 1× N20 geared motor (optional, 6 V, 50‑150 RPM; the reference picture shows the 150 RPM version).

模型可直观的观察转动、正弦、余弦的映射关系

端点的球体建议使用双色耗材打印，在不同角度观察可以有不同的颜色显示

可选择打印电动或手动组件

非3D打印配件有2个608轴承、1个N20减速电机（可选，6V ，50~150转每分钟，图片是150转每分钟）

Assembly instructions:

组装示意如下

1、Do not apply force to the end‑point spheres from the rear side of the support. Use pliers to grip the front end and press straight down vertically.

2、There are three types of supports. The one marked “Circle” is the shortest. Install the supports marked “Rectangle” and “Triangle” sequentially with a 30‑degree offset each. (Simply put: except for the first support, offset each subsequent one by 30 degrees and ensure it fits onto the shaft.)

1、端点的球体，不要从支架的后方用力，建议用钳子夹住前端垂直向下用力

2、支架分为3种，第一个标记了 “圆”，是高度最低的那个，后面按顺序依次偏移30度放置“长方形”和“三角形”标记即可。（简单的说，除了第一个，只要偏移30度，且能放进轴里面去就对了）