point of intersection
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point of intersection
The point at which two or more lines, straight lines, or curves meet and cross. This term is mainly used in geometry and mathematics.
Der Schnittpunkt der beiden Geraden wurde exakt berechnet.
The point of intersection of the two straight lines was calculated exactly.
The word is made up of 'Schnitt' (cut/intersection, from the verb 'schneiden' (to cut)) and 'Punkt' (point). So it literally describes a point at which something intersects or crosses.
An diesem Schnittpunkt treffen sich drei verschiedene Straßen.
Three different streets meet at this intersection.
You can tell from context whether the geometric or figurative meaning is intended. Words like 'Gerade' (straight line), 'Linie' (line), or 'berechnen' (to calculate) point to geometry. Terms like 'Kulturen' (cultures), 'Interessen' (interests), or 'Geschichte' (history) indicate the figurative meaning.
Wir müssen den Schnittpunkt der beiden Funktionen berechnen.
We have to calculate the point of intersection of the two functions.
In the mathematical meaning, 'Schnittpunkt' (point of intersection) is often used with the preposition 'von' (of) or 'zwischen' (between). Typical verbs are 'berechnen' (to calculate), 'bestimmen' (to determine), and 'finden' (to find).
Der Schnittpunkt von Gerade a und Gerade b liegt im negativen Bereich.
The point of intersection of line a and line b lies in the negative range.
In its figurative meaning, 'Schnittpunkt' (intersection) is often used for abstract concepts. Common combinations are 'Schnittpunkt der Kulturen' (intersection of cultures), 'Schnittpunkt der Interessen' (intersection of interests), or 'am Schnittpunkt von Kunst und Technologie' (at the intersection of art and technology).
Dieses Festival ist ein Schnittpunkt für Musiker aus aller Welt.
This festival is an intersection for musicians from all over the world.
knot / node
'der Knoten' and 'der Schnittpunkt' can both describe a place where lines, routes, or developments meet. 'der Schnittpunkt' is especially appropriate when lines really cross, for example in mathematics or in a drawing. 'der Knoten' more often means a point in a network where several connections converge. This can be in transportation, technology, or a data network. The words are easy to confuse because both have to do with intersections. As a guide: in geometry and with lines, you are more likely to say 'Schnittpunkt'; with networks and connections, you are more likely to say 'Knoten'.
Im Matheheft markiert Lisa den Schnittpunkt der beiden Geraden mit einem roten Punkt.
In her math notebook, Lisa marks the point of intersection of the two straight lines with a red dot.
Der Techniker prüft den Knoten, an dem mehrere Leitungen zusammenlaufen.
The technician checks the node where several lines come together.