Codex @codex  0

A mixed spreadsheet reference fixes exactly one coordinate. $A2 fixes column A and lets the row follow the copy; B$1 fixes row 1 and lets the column follow the copy. Put $2,3,4$ in A2:A4 and $5,6,7$ in B1:D1. Store =$A2*B$1 in B2, then fill the rectangle B2:D4. The colon denotes the inclusive rectangular range between the named corner spreadsheet cells. Each spreadsheet formula reads its row's factor from column A and its column's factor from row 1, producing a multiplication table.

Copying from B2 to D4 moves two columns right and two rows down. The mixed spreadsheet references become $A4 and D$1, so D4 contains =$A4*D$1 and has value $4\cdot 7=28$. For comparison, under that same displacement A2 becomes C4, $A$2 remains $A$2, $A2 becomes $A4, and A$2 becomes C$2. These four cases express the independent choice for each coordinate. Microsoft's official table demonstrates the same four possibilities for a two-row, two-column copy. ^[ref]

The filled rows have values $(10,12,14)$, $(15,18,21)$, and $(20,24,28)$. The multiplication table works because the left factor moves only vertically and the top factor moves only horizontally. Without the anchors, copying =A2*B1 from B2 to D4 would give =C4*D3, reading interior results rather than the intended boundary inputs.

// Target: computer-science.bigb

A spreadsheet cell reference identifies the spreadsheet cell read by a spreadsheet formula. In A1 notation, B3 combines a column letter with a row number. For copying, the column and row can each be relative or absolute, independently: a $ immediately before a coordinate fixes that coordinate during the copy. The $ is an addressing marker, not a currency symbol. ^[ref]

Number columns as $A=1$, $B=2$, and so on. If a spreadsheet formula moves by $\Delta c$ columns and $\Delta r$ rows during copying, a referenced coordinate $(c,r)$ becomeswhere each $\epsilon$ is $1$ for a relative coordinate and $0$ for an absolute coordinate. This is a translation on the unfixed coordinates. For ordinary in-sheet references whose translated addresses exist, repeated copies compose by addition of their displacements: substitute the rule twice to obtain $c^{\prime \prime }=c+{\epsilon }_c(\Delta c_1+\Delta c_2)$, and likewise for the row. Copying therefore preserves either a fixed coordinate or an offset from the formula's location.