I never understood how Einstein originally derived E = mc^2..until now!

Let's derive the most equation in physics, E = mc^2, intuitively. This is Albert Einstein's original 1905 derivation. Here we will see exactly where the c^2 in the mass energy relation really comes from. We will do each part step by step. We will also derive the expression for the relativistic doppler effect. Chapters: 00:00 Introduction 00:27 Counting energy lost by the atom 03:31 Relativistic doppler effect animation 06:35 Recounting energy from moving frame 07:20 Discovering Mass - Energy connection 09:47 How mass - energy relation comes from constant speed of light! 12:43 Rearranging the equations - (1) 13:43 Deriving relativistic doppler effect equation - intuitively 20:05 Substituting in equation (1) 22:40 Summarising the result so far 23:19 Final substitution 26:25 The climax - E = mc^2 derived 26:50 The summary