It's almost always better to avoid math and instead let the tools and materials hone perfect joinery. That usually involves nibbling up to things.
1/ Perfect half-lap joinery
Problem: Math is slow and introduces chances for error.
Solution: Let the saw dial in the depth by flipping a test piece repeatedly until the setting is perfect.
2/ Cleaner cuts on a table saw for long tapers
Problem: When ripping hardwood, a slow feed rate causes burns on the cut edge
Solution: Cut the piece about 1/16 inch too wide with the slow feed rate, and then run the workpiece through the saw slicing the last 1/16-inch off. This light pass at the end allows you to feed the stock much quicker, eliminating the burned edge.
They use a tapering sled/jig in the video example and insert 1/16-inch shims to set up the initial cut. After the cut is set up, they remove the shims so that the workpiece will be 1/16-inch too wide after the cut. Now, return the shims and cut the piece to size, sliding the wood through the saw quickly and with no burn marks.
3/ Dialing in Dadoes
Problem: It is challenging to cut tongues and tenons to fit dadoes and grooves.
Solution: Cutt the dado first. If you cannot cut the dado first, use painter's tape as a shim to slightly move the router bit, embiggening* the width of the dado or groove.
This concept can be applied to many situations where micro-adjustments are needed.
4/ Cutting perfectly-sized dadoes or grooves using a drill bit
Problem: Same as above, only different. If you use the stock that needs to fit the dado as a spacer against a stop block on a tablesaw sled, the dado will be exactly one saw kerf too wide.
Solution: Same as above, but also different. The workpiece must be offset from the stop block by a saw blade thickness to cut the second dado edge. A 1/8-inch drill bit makes an excellent spacer between the stop block and the workpiece in almost all cases.
Bonus tip: Use a saw blade with a flat tooth to end up with a flat dado.
