Bleaug claims the following:
Almost a pure geometric proof this time (only requires Pythagorean theorem).
- TIJ is the section of the pyramid by a plane orthogonal to base and parallel to BC and AD
- by construction, TI is orthogonal to AB, and TJ to CD
- hence: AT^2-BT^2 = AI^2+IT^2-BI^2-IT^2 = AI^2-BI^2, similarly DT^2-CT^2 = DJ^2-CJ^2
- since AIB is a translation of DJC: AT^2-BT^2 = DT^2-CT^2
- from which we get DT^2 = AT^2-BT^2+CT^2 = 9-2+1 = 8
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