javascript prototype chain: Rectangle.prototype = new Shape() or Rectangle.prototype = Shape?

I saw two different patterns and explanations. One from DailyJS and many others: Rectangle.prototype = new Shape();

and then there's Crockford's here which implies just Rectangle.prototype = Shape;

Now theory-wise, why you need to run the 'new'? it runs the constructor function, yes. it also assigns the Rectangle's prototype the Shape's prototype. but we should be able to do inheritance just with a simple assignment of the parent into the prototype.

I wondered if the reason is prototype chaining. it seems, that in case 1, it will create a prototype chain. Meaning, that the Rectangle prototype will have the Shape prototype. In the second case, the Rectangle's prototype will just have Shape's methods - but not Shape's prototype methods.

Is that right? many thanks for any thoughts.

Crockford which implies just Rectangle.prototype = Shape;

I can't really see that.

Now theory-wise, why you need to run the 'new'? it runs the constructor function, yes.

Yet we actually don't need (want) that, we only need the inheritance from Shape.prototype

it also assigns the Rectangle's prototype the Shape's prototype.

Not really. new Shape creates a new object which inherits from Shape.prototype, that's what matters us. You've got that right.

In the second case, the Rectangle's prototype will just have Shape's methods - but not Shape's prototype methods.

Yes, that's correct. You should inherit from Shape.prototype - but via Object.create(Shape.prototype), not by creating an instance. See JavaScript inheritance: Object.create vs new or What is the reason [not] to use the 'new' keyword here?. This is what Crockford actually does - and even before Object.create was introduced by EcmaScript 5.1, he found a clever way to do that with his helper function

function object(o) {
    function F() {}
    F.prototype = o;
    return new F();
}

which is now the common shim for Object.create in browsers that don't support it natively.