feat: add Pi approximation using Leibniz formula

Maths/PiApproximation.js

@@ -0,0 +1,22 @@
+/**
+ * @function leibnizPi
+ * @description Approximates Pi using the Leibniz formula:
+ *   π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...
+ * @param {number} terms - Number of terms to use in approximation
+ * @returns {number} - Approximation of Pi
+ * @see https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80
+ * @example leibnizPi(1000) => ~3.1405926...
+ * @example leibnizPi(10000) => ~3.1414926...
+ */
+const leibnizPi = (terms) => {
+  if (!Number.isInteger(terms) || terms < 1) {
+    throw new TypeError('Input must be a positive integer')
+  }
+  let sum = 0
+  for (let i = 0; i < terms; i++) {
+    sum += (-1) ** i / (2 * i + 1)
+  }
+  return 4 * sum
+}
+
+export { leibnizPi }

Maths/test/PiApproximation.test.js

@@ -0,0 +1,46 @@
+import { leibnizPi } from '../PiApproximation.js'
+
+describe('leibnizPi', () => {
+  test('leibnizPi(1) returns 4', () => {
+    expect(leibnizPi(1)).toBe(4)
+  })
+
+  test('leibnizPi(2) returns 2.666...', () => {
+    expect(leibnizPi(2)).toBeCloseTo(2.667, 2)
+  })
+
+  test('leibnizPi(100) approximates pi', () => {
+    expect(leibnizPi(100)).toBeCloseTo(3.13, 1)
+  })
+
+  test('leibnizPi(1000) approximates pi more closely', () => {
+    expect(leibnizPi(1000)).toBeCloseTo(3.14, 2)
+  })
+
+  test('leibnizPi(10000) approximates pi even more closely', () => {
+    expect(leibnizPi(10000)).toBeCloseTo(3.1415, 3)
+  })
+
+  test('more terms give better approximation', () => {
+    const pi = Math.PI
+    expect(Math.abs(leibnizPi(10000) - pi)).toBeLessThan(
+      Math.abs(leibnizPi(100) - pi)
+    )
+  })
+
+  test('throws TypeError for zero', () => {
+    expect(() => leibnizPi(0)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => leibnizPi(-100)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => leibnizPi(100.5)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for string input', () => {
+    expect(() => leibnizPi('100')).toThrow(TypeError)
+  })
+})