From Circles to Squares - This animation shows how a Fourier series builds a square wave. Starting smooth and wavy, each added harmonic sharpens the shape until it forms the classic square wave. | The Brain Maze

Fourier series allow us to represent periodic functions as infinite sums of sine and cosine terms. Remarkably, they can approximate discontinuous functions like the square wave with increasing accuracy as more terms are added. This method reveals deep connections between analysis and signal processing, and is widely used in physics, engineering, and audio synthesis. تمكننا متسلسلات فورييه من تمثيل الدوال الدورية كمجموع لا نهائي من حدود الجيب وجيب التمام. ومن المدهش أنها تستطيع تقريب دوال غير مست

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