Exact energy triangles show how rest energy, pc, total energy, and kinetic energy move together. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Mass four at speed three totals one hundred twenty five joules

The first triangle uses mass 4 kg and speed 3 m/s. Rest energy is 100 J, motion leg pc is 75 J, and total energy is 125 J.

1002+752=1252K=125100=25100^2+75^2=125^2\quad K=125\,-\,100=25
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energykinetic energy

Mass three at speed four reaches the same total another way

The second row lowers mass to 3 kg and raises speed to 4 m/s. Rest energy becomes 75 J, pc becomes 100 J, and the same total 125 J closes the triangle.

752+1002=1252K=12575=5075^2+100^2=125^2\quad K=125\,-\,75=50
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energykinetic energy

Doubling the fast mass doubles every energy leg

Keeping speed 4 m/s and doubling mass to 6 kg doubles the second row: rest energy 150 J, pc 200 J, total 250 J, and kinetic energy 100 J.

1502+2002=2502K=250150=100150^2+200^2=250^2\quad K=250\,-\,150=100
Relativistic energyRest energy and motion energy form a triangle.speedquiet leglimitbetagammarest energymotion energytotal energykinetic energy